Hey there! I have a doubt from Combinatorics! If u can please help me with it that would be great!!!

A basketball squad of 10 must be chosen from a group of 8 women and 6 men. How many squads are possible:

a) without restriction?

b) if the squad contains 6 women and 4 men?

c) if the squad must contain at least 6 women?

d) if the squad contains all men?

Now I managed to figure out that this is a "combination" question. I managed to do question a but not b, c and d.

Thanks, much appreciated .

I'm not too great with combinatorics. I could be wrong, so if someone with a little more experience could check this, that'd be great.

**Part a**We need to choose 10 players from a group of 14: \[\binom{14}{10}=1001\ \text{ possible squads}\]

**Part b**We need to choose 6 women from 8

*and* 4 men from 6: \[\binom{8}{6}\binom{6}{4}=420\ \text{ possible squads}\]

**Part c**We could either choose 6 women and 4 men, 7 women and 3 men, or, 8 women and 2 men: \[\binom{8}{6}\binom{6}{4}+\binom{8}{7}\binom{6}{3}+\binom{8}{8}\binom{6}{2}=595\ \text{ possible squads}\]

**Part d**The wording to this question doesn't seem correct. It's

**impossible** to pick a squad so that all 10 members are men since there are only 6 men to pick from. I believe you meant

*"if the squad contains all the men"*, in which case, we would need to select 4 women from 8

*and* 6 men from 6: \[\binom{8}{4}\binom{6}{6}=70\ \text{ possible squads}\]