Question

Combination Question

A delegation of 4 people is to be formed from 5 married couples. Find the number of ways in which the delegation can be chosen if it contains:
i) 2 married couples.
ii) At least one man and one woman.
iii) no married couples.

Answer and brief working out would be appreciated!

Answer 1

xxxx

4 spaces to fill

i) 2 married couples.
5c2

Answer 2

cuz, 2 couples will fill 4 spaces

Answer 3

ii) At least one man and one woman.
total - (all men + all women)
10c4 - (5c4 + 5c4)

Answer 4

iii) no married couples.
total - only married couple
10c4 - 5c2

Answer 5

I think you're wrong for part ii) and part iii) because you forgot to include the cases where there are some men/some women/some married couples?

My answers are:
ii) 5C1*5C1*8C2
iii)10C4-(5C1*8C2)-5C2

Can someone confirm?