Answer with explanation:
Given : Number of men = 4
Number of women = 6
Total people = [tex]6+4=10[/tex]
Total number of ways to make a committee of five people from 10 persons :-
[tex]^{10}C_{4}=\dfrac{10!}{4!(10-4)!}=210[/tex]
a) Number of ways to make committee that has exactly four women :
[tex]^6C_4\times ^4C_1=\dfrac{6!}{4!(6-4)!}\times4=60[/tex]
The  probability that committee has exactly four women :
[tex]\dfrac{60}{210}=\dfrac{2}{7}[/tex]
b) Number of ways to make committee that has at-least four women :
[tex]^6C_4\times ^4C_1+^6C_5=\dfrac{6!}{4!(6-4)!}\times4+6=66[/tex]
The probability that committee at-least four women :
[tex]\dfrac{66}{210}=\dfrac{22}{70}[/tex]
c) Number of ways that committee has more than 4 women :-
[tex]^6C_5\times^4C_0=6[/tex]
The probability that committee has more than 4 women :-
[tex]\dfrac{6}{210}[/tex]
Now, the  probability that committee has at most four women :-
[tex]1-\dfrac{6}{210}=\dfrac{204}{210}=\dfrac{102}{105}[/tex]
