Astudent club has seven members. 3 are to be chosen to go together to a national meeting. a) how many distinct groups of 3 can be chosen? b) if the student club contains 4 men and 3 women, how many distinct groups of 3 contain two men and one woman?

1) 35 distinct groups can be formed.

2) 18  distinct groups can be formed containing 2 men and 1 woman.

Step-by-step explanation:

The no of groups of 3 members that can be chosen from 7 members equals no of combinations of 3 members that can be formed from 7 members.

Thus no of groups =

thus 35 distinct groups can be formed.

Part b)

Now since the condition is that we have to choose 2 men and 1 women to form the group

let A and B be men member's of group thus we have to choose 2 member's from a pool of 4 men which equals

Let the Woman member be C thus we have to choose one woman from a pool of 3 women hence number of ways in which it can be done equals 3.

thus the group can be formed in different ways.

a negative exponent is translated as follows:

so, we have