Question

A company has $5$ men and $6$ women. What are the number of ways of selecting a group of eight persons?

• A. $165$
• B. $185$
• C. $205$
• D. $225$

Answer 1

The correct option is A $165$

The number of ways of selecting a group of eight is

5 men and 3 women=${}^5{C}_5{\times }^6{C}_3$ =20

4 men and 4 women=${}^5{C}_4{\times }^6{C}_4$ =75

3 men and 5 women=${}^5{C}_3{\times }^6{C}_5$=60

2 men and 6 women=${}^5{C}_2{\times }^6{C}_6$=10

Thus the total possible cases is 20+75+60+10=165.

Option A is correct answer.