COMBINATIONS

1A. In how many ways can a committee of 2 can be formed from a group of 5 ?

1) 12 2) 10 3)15 4)25 5) None of these

1B. In how many ways can a committee of 3 can be formed from a group of 6 ?

1)12 2) 16 3)20 4)24 5) None of these

1C. In how many ways can a committee of 2 can be formed from a group of 6 ?

1) 15 2)20 3)24 4) 18 5) None of these

1D. In how many ways can a committee of 4 can be formed from a group of 7 ?

1)25 2)30 3)32 4)35 5) None of these

2A. How many triangles can be formed by joining the vertices of a heptagon ?

1)25 2)32 3)35 4)40 5) None of these

2B. How many quadrilaterals can be formed by joining the vertices of a hexagon ?

1) 10 2)12 3)15 . 4)18 5) None of these

2C. How many pentagons can be formed by joining the vertices of a heptagon ?

1) 12 2) 18 3)21 4)24 5) None of these

2D. How many hexagons can be formed by joining the vertices of a nonagon ?

1) 84 2) 72 3)68 4)64 5) None of these

3A In how many ways can a committee consisting of 3 men and 2 women be formed from a group of 7 men and 5 women?

1)256 2)350 3)384 4)420 5) None of these

3B. In how many ways can a committee consisting of 1 man and 1 woman be formed from a group of 3 men and 2 women?

1)2 2) 4 3)8 4)6 5) None of these

3C. In how many ways can a committee consisting of 2 men and 1 woman be formed from a group of 5 men and 3 women?

1)20 2)24 3)30 4)32 5) None of these

3D. In how many ways can a committee consisting of 4 men and 2 women be formed from a group of 7 men and 5 women?

1) 320 2)350 3)360 4)392 5) None of these

4A. From a bag containing 6 red balls and 4 blue balls in how many ways can 4 red balls and 3 blue balls be chosen ?

1)48 2)60 3)72 4)120 5) None of these

4B. From a bag containing 4 red balls and 3 blue balls in how many ways can 2 red balls and 1 blue balls be chosen ?

1) 12 2) 15 3)18 4)24 5) None of these

4C. From a bag containing 5 red balls and 4 blue balls in how many ways can 3 red balls and 3 blue balls be chosen ?

1) 30 2)32 3)36 4)40 5) None of these

4D. From a bag containing 5 red balls and 6 blue balls in how many ways can 2 red balls and 3 blue balls be chosen ?

1) 120 2)144 3)200 4)240 5) None of these

5A Out of 5 men and 4 women, a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include atleast 2 women.

1) 100 2)105 3)108 4) 112 5) None of these

5B. Out of 3 men and 2 women, a committee of 3 is to be formed. Find the number of ways in which this can be done so as to include atleast 1 woman.

1) 9 2) 12 3)15 4) 18 5) None of these

5C. Out of 4 men and 3 wortre'n, a committee of 3 is to be formed.Find the number of ways in which this can be done so as to include atleast 1 woman.

1) 20 2)25 3)31 4)36 5) None of these

5D. Out of 6 men and 5 women, a committee of 4 is to be formed.Find the number of ways in which this can be done so as to include atleast 2 women

1)200 2)208 3)212 4)215 5) None of these

6A.In how many ways can one or more of 5 friends be invited for dinner ?

1)31 2) 32 3) 36 4)40 5) None of these

6B.In how many ways can one or more of 3 fnends be invited for dinner ?

1)5 2)6 3) 7 4)8 5) None of these

6C.In how many ways can one or more of 7 fnends be invited for dinner ?

1)127 2) 132 3)144 4) 156 5) None of these

6D. In how many ways can one or more of 8 fnends be invited for dinner ?

1)240 2)246 3)252 4)255 5) None of these

7A.In a group of 16 persons, each person shakes hand with each other In total how many shakehands will be taken place?

1)100 2)120 3)150 4) 140 5) None of these

7B. In a group of 20 persons, each person shakes hand with each other In total how many shakehands will be taken place?

1)380 2)320 3)240 4)190 5) None of these

7C. In a group of 25 persons, each person shakes hand with each other. In total how many shakehands will be taken place?

1)600 2)420 3)300 4)240 5) None of these

7D. In a group of 75 persons, each person shakes hand with each other. In total how many shakehands will be taken place?

1)5550 2)4220 3)2775 4)2420 5) None of these

8A.55 games were played at a chess tournament with each contestant plays once against each of the others. How many participants were there ?

1)9 2)10 3)11 4)12 5) None of these

8B.45 games were played at a chess tournament with each contestant plays once against each of the others. How many participants were there ?

1) 9 2)10 3) 11 4)12 5) None of these

8C. 120 games were played at a chess tournament with each contestant plays once against each of the others. How many participants were there ?

1) 12 2) 16 3)20 4)24 5) None of these

8D. 5050 games were played at a chess tournament with each contestant plays once against each of the others. How many participants were there ?

1)95 2)99 3)100 4)101 5) None of these

9A. In how many ways can 3 scholarships of equal value be awarded to 10 candidates

1)120 2)96 3) 144 4)80 5) None of these

9B. In how many ways can 2 scholarships of equal value be awarded to 5 candidates?

1)20 2)18 3)16 4) 10 5) None of these

9C. In how many ways can 4 scholarships of equal value be awarded to 6 candidates?

1)30 2)18 3) 15 4)10 5) None of these

9D. In how many ways can 3 scholarships of equal value be awarded to 12 candidates

1)220 2)240 3)320 4)360 5) None of these

10A. In how many ways can 5 players be chosen from 12 players so as to include one particular player ?

1)320 2) 330 3) 356 4) 360 5) None of these

10B. In how many ways can 4 players be chosen from 10 players so as to include one particular player ?

1)84 2)72 3) 64 4)60 5) None of these

10C. In how many ways can 6 players be chosen from 15 players so as to exclude one particular player ?

1)15015 2) 3003 3)150150 4) 30030 5) None of these

10D. In how many ways can 5 players be chosen from 16 players so as to exclude one particular player ?

1)15015 2) 3003 3)150150 4) 30030 5) None of these

11A. A cricket 11 is to be chosen out of 16 players of whom 6 are bowlers and 3 are wicket keepers. In how many ways can this be done if the 11 is to contain 4 bowlers and 2 wicket keepers ?

1)895 2) 925 3)945 4)965 5) None of these

11B. A cricket 11 is to be chosen out of 16 players of whom 5 are bowlers and 4 are wicket keepers. In how many ways can this be done if the 11 is to contain 4 bowlers and 2 wicket keepers ?

1)630 2)642 3) 720 4) 756 5) None of these

11C. A cricket 11 is to be chosen out of 20 players of whom 8 are bowlers and 5 are wicket keepers. In how many ways can this be done if the 11 is to contain 5 bowlers and 2 wicket keepers ?

1) 9800 2) 10800 3)14400 4)19600 5) None of these

11D. A cricket 11 is to be chosen out of 18 players of whom 8 are bowlers and 5 are wicket keepers In how many ways can this be done if the 11 is to contain 5 bowlers and 3 wicket keepers ?

1)2800 2) 11200 3) 5600 4) 8400 5) None of these

12A. In a shelf there are 10 English and 8 Telugu books. In how many ways can 6 English books and five Telugu books be chosen,if a partcular English book is to be excluded?

1)4704 2)4408 3)4602 4)4047 5) None of these

12B. In a shelf there are 8 English and 6 Telugu books. In how many ways can 6 English books and do books be chosen,if a partcular English book is to be excluded?

1) 96 2) 100 3)105 4) 108 5) None of these

12C In a shelf there are 9 English and 6 Telugu books. In how many ways can 6 English books and three Telugu books be chosen,if a partcular Telugu book is to be excluded?

1) 720 2) 840 3) 960 4) 1080 5) None of these

12D. Ina shelf there are 10 English and 7 Telugu books. In how many ways can 7 English books and four Telugu books be chosen,if a partcular English book is to be excluded and a particular Telugu book is to be included ?

1)640 2)680 3)704 4)720 5) None of these

13A. Out of 5 teachers and 6 boys, a committee of 6 is to be selected. Find the number of ways in which this can be done when there is a majority of teachers.

1) 81 2)76 3)72 4)68 5) None of these

13B. Out of 5 teachers and 4 boys, a committee of 6 is to be selected. Find the number of ways in which this can be done when there is a majority of teachers.

1)25 2) 30 3)34 4)38 5) None of these

13C. Out of 6 teachers and 4 boys, a committee of 7 is to be selected. Find the number of ways in which this can be done when there is a majority of teachers.

1) 84 2)100 3)108 4) 120 5) None of these

13D Out of 7 teachers and 5 boys, a committee of 9 is to be selected. Find the number of ways in which this can be done when there is a majority of teachers.

1) 120 2) 144 3)156 4) 185 5) None of these

14A There are 3 questions in 1st section, 3 questions in the 2nd section and 2 questions in the 3rd section in question paper of an examination. In how many ways can a student who appeared for the examination select to answer any five questions of the paper choosing atleast one question from each section ?

1) 36 2)40 3)44 4)48 5) None of these

14B There are 5 questions in 1st section and 3 questions in the 2nd section in question paper of an examination. In how many ways can a student who appeared for the examination select to answer any five questions of the paper choosing atleast two questions from each section ?

1) 32 2)40 3)48 4)56 5) None of these

14C. There are 4 questions in 1st section, 4 questions in the 2nd section and 3 questions in the 3rd section in question paper of an examination. In how many ways can a student who appeared for the examination select to answer any five questions of the paper choosing atleast one question from each section ?

1) 320 2) 346 3) 364 4) 382 5) None of these

14D. There are 5 questions in 1st section, 4 questions in the 2nd section and 3 questions in the 3rd section in question paper of an examination.In how many ways can a student who appeared for the examination select to answer any eight questions of the paper choosing atleast two questions from each section ?

1) 320 2) 340 3)360 4)420 5) None of these

15A.A party of 9 persons are to travel in two vehicles,one of which will not hold more than seven and the other not more than four.in how many ways can the party travel?

1) 123 2) 234 3) 246 4) 468 5) None of these

15B.A party of 9 persons are to travel in two vehicles,one of which will not hold more than six and the other not more than four.in how many ways can the party travel?

1) 210 2) 165 3) 120 4) 108 5) None of these

15C.A party of 10 persons are to travel in two vehicles,one of which will not hold more than seven and the other not more than four.in how many ways can the party travel?

1) 220 2) 246 3) 258 4) 330 5) None of these

15D.A party of 10 persons are to travel in two vehicles,one of which will not hold more than seven and the other not more than five.in how many ways can the party travel?

1) 560 2) 576 3) 582 4) 594 5) None of these