Question

Find the number of ways in which a committee of 4 can be chosen from six boys and

six girls if it must contain at least one boy and one girl.​

Answer 1

465 ways

Step-by-step explanation:

Atleast 1 girl and 1 boy

Possible combinations :

1 girl ; 3 boys = 6C1 ; 6C3

2 girls ; 2 boys = 6C2 ; 6C2

3 girls ; 1 boy = 6C3 ; 6C1

(6C1 * 6C3) + (6C2 * 6C2) + (6C3 * 6C1)

Combination formula:

nCr = n! ÷ (n-r)!r!

We can also use a calculator :

6C1 = 6

6C3 = 20

6C2 = 15

Hence,

(6C1 * 6C3) + (6C2 * 6C2) + (6C3 * 6C1)

(6 * 20) + (15 * 15) + (20 * 6)

120 + 225 + 120

= 465 ways