Question

A committe of 5 members is to be formed out of 6 gents and 4 ladies. In how many ways

this can be done, when atleast two ladies are included?​

Answer 1

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=186Hence, the required number of ways =(120+60+6)=186. or (ii) (2 ladies out of 4) and (3 men out of 6).

Answer 2

Answer:

Hey there,

The number of ways is 186, as noted in other answers. Here's another way to do it: take all possible ways of choosing five people, and subtract the ways that are all five men or four men and one woman: 10565406441 =186.

But more importantly, an answer to your second question. The reason (42)(83) is wrong is because you double count certain combinations. Remember when you multiply (42)=6 and (83)=56 and claim that gives you the answer, you're saying for each of the 6 ways of choosing two women, there are 56 ways of choosing the rest, each of which results in a unique combination.