Question

How would i solve a problem like this?

i'm confused on how probability works with combinations, could someone explain using this example? thanks!

Answer 1

A committee of 5 has more boys than girls if it consists of

• 3 boys and 2 girls,

• 4 boys and 1 girl, or

• 5 boys

In the first case, there are

`\dbinom73 \dbinom62 = 525`

possible committees. In the second case,

`\dbinom74 \dbinom61 = 210`

In the third case,

`\dbinom75 \dbinom60 = 21`

So there is a total of

`\dbinom73\dbinom62 + \dbinom74\dbinom61 + \dbinom75\dbinom60 = \boxed{756}`

possible committees containing more boys than girls.