Question

From a council of $7$ Hindus, $5$ Muslims and $4$ Christians a committee of $5$ is to be formed with $1$ Christian and at least two Hindus. The number of ways of forming the committee is

• A. 1220
• B. 1240
• C. 1680
• D. 1280

Answer 1

The correct option is C 1680

Case 1) $1$ Christian, $2$ Hindus, $2$ Muslims
Number of ways ${=}^4{C}_1{\times }^7{C}_2{\times }^5{C}_2$
Case 2) $1$ Christian, $3$ Hindus, $1$ Muslims
Number of ways ${=}^4{C}_1{\times }^7{C}_3{\times }^5{C}_1$
Case 3) $1$ Christian, $4$ Hindus, $0$ Muslims
Number of ways ${=}^4{C}_1{\times }^7{C}_4$
Total number of ways: ${=}^4{C}_1{\times }^7{C}_2{\times }^5{C}_2{+}^4{C}_1{\times }^7{C}_3{\times }^5{C}_1{+}^4{C}_1{\times }^7{C}_4=1680$