Question

In how many ways a committee of 6 persons can be formed out of 5 men
and 6 women such that women are in majority?

Answer 1

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MATHS

A committee of 5 is to be formed out of 6 gents and 4 ladies. in how many ways this can be done, if at most two ladies are included?

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ANSWER

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

3

×

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