Question

A club consisting of 6 men and 8 women will choose a committee of 4. In how many ways

Answer 1

Answer:

The number of ways the committee be chosen is 295 ways.

Step-by-step explanation:

There are 6 men and 8 women.

A committee of 4, in which there must be at least 1 woman.

Let W- woman. M - man

So the combinations are: 1W, 3M or 2W, 2M or 3W, 1M or 4W

Now we have to use the combination formula and find the answer.

nCr = $\frac{n!}{r!(n-r)!}$

Using the above formula, we can find the answer.

4C1 × 7C3 + 4C2×7C2 + 4C3×7C1 + 4C4

= $= \frac{4!}{1!(4-1)!} .\frac{7!}{3!(7-3)!} +\frac{4!}{2!(4 -2)!} .\frac{7!}{2!(7 -2)!} + \frac{4!}{3!(4 -3)!} .\frac{7!}{1!(7-1)!} +\frac{4!}{4!(4-4)!}$

Simplifying the above factorials, we get

=4×35 + 6×21 + 4×7 + 1

= 140+126+28+1

= 295

The number of ways the committee be chosen is 295 ways.