Question

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways is :

• A. 1050
• B. 1625
• C. 560
• D. 575

Hint:

Break down problems with multiple constraints into mutually exclusive cases and sum the results.

Answer 1

The Correct Option is B

Step 1: Case 1: 2 Ind, 4 For $\Rightarrow ^6C_2 \times ^8C_4 = 15 \times 70 = 1050$.
Step 2: Case 2: 3 Ind, 6 For $\Rightarrow ^6C_3 \times ^8C_6 = 20 \times 28 = 560$.
Step 3: Case 3: 4 Ind, 8 For $\Rightarrow ^6C_4 \times ^8C_8 = 15 \times 1 = 15$.
Step 4: Total = $1050 + 560 + 15 = 1625$.