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, the committee can be formed is ______.

Options

• 560

• 1050

• 1625

• 575

Answer 1

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 1625.

Explanation:

Given: 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.

There are multiple cases to satisfy the given criteria. The committee can consist of (2I, 4F), (3I, 6F) or (4I, 8F) where I represent Indians and F represents foreigners.

3 Indians from 6 Indians can be selected in ⁶C₃ ways

6 foreigners out of 8 can be selected in ⁸C₆ ways.

Similarly, we can find the number of ways in all other cases.

So, the total number of ways in which a committee can be formed = ⁶C₂ × ⁸C₄ + ⁶C₃ × ⁸C₆ + ⁶C₄ × ⁸C₈

= 15 × 70 + 20 × 28 + 15 × 1

= 1050 + 560 + 15

= 1625