Respuesta :
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 = [tex]\frac{n!}{r!(n-r)!}[/tex]
Using the above formula, we can find the answer.
4C1 × 7C3 + 4C2×7C2 + 4C3×7C1 + 4C4
= [tex]= \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)!}[/tex]
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.
