Question

There are 7 men and 3 ladies. Find the number of ways in which a committee of 6 can be formed of them if the committee is to include at least two ladies?

Answer 1

There can be two ways to form a committee if the committee is to include at least two ladies.

First, there will be 2 ladies and 4 men.
Second, there will be 3 ladies and 3 men.

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Answer 2

Answer:

The number of ways in which the committee can be formed is 140.

Step-by-step explanation:

Given that there are 7 men and 3 ladies.

We need to form a committee of 6 members. Also, that committee should include two ladies at least.

There are different ways to do this.

1) Committee can have 2 ladies and 4 men.

The number of ways is,

$3C_2\times 7C_4=\dfrac{3!}{2!(3-2)!}\times \dfrac{7!}{4!(7-4)!}=3\times \dfrac{7\times 6\times 5}{2\times 3}= 105$

2) Committee can have 3 ladies and 3 men.

The number of ways is,

$3C_3\times 7C_3=\dfrac{3!}{3!}\times \dfrac{7!}{3!(7-3)!}= \dfrac{7\times 6\times 5}{2\times 3}= 35$

So the total number of ways = 105+35=140