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Question 62

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, the committee can be formed, is:

We need to form a scientific committee from 6 Indians and 8 foreigners, with at least 2 Indians, and the number of foreigners must be double the number of Indians.

If we select $$k$$ Indians, then we must select $$2k$$ foreigners. We need $$k \geq 2$$, $$k \leq 6$$, and $$2k \leq 8$$, so $$k$$ can be 2, 3, or 4.

For $$k = 2$$: we choose 2 Indians from 6 and 4 foreigners from 8. This gives $$\binom{6}{2} \times \binom{8}{4} = 15 \times 70 = 1050$$.

For $$k = 3$$: we choose 3 Indians from 6 and 6 foreigners from 8. This gives $$\binom{6}{3} \times \binom{8}{6} = 20 \times 28 = 560$$.

For $$k = 4$$: we choose 4 Indians from 6 and 8 foreigners from 8. This gives $$\binom{6}{4} \times \binom{8}{8} = 15 \times 1 = 15$$.

The total number of ways is $$1050 + 560 + 15 = 1625$$.

Hence, the correct answer is Option B.

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