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Question

The law firm has 8 female and 10 male lawyers. The committee of 5 which have 3 female and 2 male lawyers is being selected to be a represent the firm office. How many committees are possible?

Answer 1

In law firm has 8 females and 10 male lawyers .

A Committee of 5 which have 3 female and 2 male lawyers has to be formed with the available members .

10 men for the first position. 

9 men for the 2nd position. 

But any two men can be arranged 2 ways (i.e. if we choose A then B, or B then A, either way it is the same committee), 

so the number of combinations of men is 10*9/2 = 45

Mathematically ,

We  have to select 2 men from 10 male lawyers  = 10c₂ = 10*9/2 = 45 .

8 women for the first position 

7 women for the 2nd position 

6 women for the 3rd position 

But any 3 women can be arranged 6 ways (i.e. ABC, ACB, BAC, BCA , CBA, CAB) .

So the number of combinations of women is 8*7*6/(6) = 56 

Mathematically ,

We  have to select 2 men from 10 male lawyers  = 8c₃ = 8*7*6/(3*2*1) = 56  .

So total combinations = 45 * 56 = 2520 .

So the  possible number of  committees  are 2520 .