Permutation and Combination

1.		Out of 2 Women and 5 Men, a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included in the committee?

10

15

25

30

2.		How many words can be formed from the letters of the word "ENGINEERING", so that vowels always come together?

4200

2100

5040

2520

3.		In how many ways can a group of 4 boys and 2 girls be formed out of a total of 7 boys and 4 girls?

210

120

224

420

4.		Out of 2 men, 3 women, 4 girls and 5 boys, in how many ways can we form a group of three people such that a boy and a girl will not be together in the group?

210

204

168

194

5.		In how many ways can 3 boys and 4 girls be arranged in a row such that boys occupy at the ends?

420

360

840

720

6.		5 people are to be arranged in a circle. Find the number of ways such that two particular persons never stand together.

18

15

12

8

7.		Find the number of squares on a chessboard?

204

200

256

128

8.		In how many ways 4 persons can be seated on 4 chairs?

20

24

26

120

9.		In how many ways can 3 prizes be distributed among 4 boys, if no boy gets more than one prize?

12

16

24

32

10.		In how many ways can 6 similar toffees be distributed to 4 children, such that every child receives at least one toffee?

10

15

18

12