There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?

Since, no order to the committee is mentioned, a combination instead of a permutation is used.
Let's sort out what we have and what we want.
Have: 5 women, 6 men.
Want: 3 women AND 1 man.
The word AND means multiply.
Woman and Men

$$\eqalign{ & ^{{\text{have}}}{{\text{C}}_{{\text{want}}}}{ \times ^{{\text{have}}}}{{\text{C}}_{{\text{want}}}} \cr & { = ^5}{{\text{C}}_3}{ \times ^6}{{\text{C}}_1} \cr & = 60 \cr} $$