Question

A committee of 8 is to be selected out of 6 males and 8 females. In how many ways it be formed so that the males may not be out numbered.

Answer 1

Answer

In 2974 ways the committee can be formed.

Given

• There are 6 males and 8 females .

To Determine

• In how many ways the committee can be formed so that males may not be out numbered.

Solution

Let us create a chart for the selection of members for committe

$\sf Male\: (6) \: \: \: \: \: \: \: \: \: Female (8) \\\\ \sf 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \\\\ \sf 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \\\\ \sf 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 \\\\ \sf 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4 \\\\ \sf 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5$

Thus , the selection can be made as,

$\sf\dashrightarrow ^{6} C_{5} \times ^{8}C_{1} + ^{6}C_{4} \times ^{8}C_{2} + ^{6}C_{3} \times ^{8}C_{3} + ^{6}C_{2} \times ^{8}C_{4} +^{6}C_1 \times ^{8}C_{5} \\\\ \dashrightarrow \sf 48 + 420 + 1050+1120+336 \\\\ \sf \dashrightarrow 2974$