Question

Find the number of ways in which a committee of 6 can be formed from 15 people if 2 are always there as head of committee.

Answer 1

A committee of 5 persons, consisting of at most two ladies, can be done in the following ways:

(a)Selecting 5 gents only out of 6. This can be done in 6 C 5 ways.

(b)Selecting 4 gents only out of 6 and 1 lady out of 4. This can be done in

6 C 4 ×4C 1 , ways.

(c)Selecting 3 gents only out of 6 and 2 ladies out of 4. This can be done in

6 C × 4 C 2

ways.

Since the committee is formed in each case, so, the total number of ways of forming the committee

=

6

C

5

+

6

C

4

×

4

C

1

+

4

C

2

=6+60+120=186

Answer 2

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