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:

Question

Aicharya · Accepted Answer

Indians Foreigners Number of ways 2 4 C 2 6 &#215; C 4 8 = 1050 3 6 C 3 6 &#215; C 6 8 = 560 4 8 C 4 6 &#215; C 8 8 = 15 Total number of ways = 1625

Indians	Foreigners	Number of ways
$2$	$4$	${}^{6}C_{2} \times {}^{8}C_{4} = 1050$
$3$	$6$	${}^{6}C_{3} \times {}^{8}C_{6} = 560$
$4$	$8$	${}^{6}C_{4} \times {}^{8}C_{8} = 15$

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians…

Solution