Well heres what I did

(8 choose 4) x (6 choose 4) = 70 x 15 = 1050

(14 choose 8) = 3003

so the probability = 1050/3003.

I dont know if thats right though

Yes, that's fine since any group of 4 men can go with any group of 4 women,

which is why the selections are multiplied.

**(ii)**
At most 1 woman is 1 woman or no women,

which means 1 woman and 7 men or all 8 men.

\(\displaystyle P=\frac{\binom{8}{7}\binom{6}{1}+\binom{8}{8}\binom{6}{0}}{\binom{14}{8}}\)

**(iii)**
If the group contains the oldest person and excludes the youngest person,

then the oldest person can go with 7 of the remaining 12.

The number of ways this can happen is \(\displaystyle \binom{12}{7}\)

hence \(\displaystyle P=\frac{\binom{12}{7}}{\binom{14}{8}}\)