A scientific committee is to formed from
Question:

A scientific committee is to 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:

1. (1) 560

2. (2) 1050

3. (3) 1625

4. (4) 575

Correct Option: , 3

Solution:

$(2 \mathrm{I}, 4 \mathrm{~F})+(3 \mathrm{I}, 6 \mathrm{~F})+(4 \mathrm{I}, 8 \mathrm{~F})$

$={ }^{6} \mathrm{C}_{2}{ }^{8} \mathrm{C}_{4}+{ }^{6} \mathrm{C}_{3}{ }^{8} \mathrm{C}_{6}+{ }^{6} \mathrm{C}_{4}{ }^{8} \mathrm{C}_{8}$

$=15 \times 70+20 \times 28+15 \times 1$

$=1050+560+15=1625$