Question

The number of different ways in which a committee of 4 members formed out of 6 Asians, 3 Europeans and 4 Americans if the committee is to have atleast one from each of the 3 regional groups is:

• A. $320$
• B. $340$
• C. $360$
• D. $380$

Answer 1

Answer: (C)

$360$

ASIANS (6) EUROPEANS (3) AMIRICANS (4)
1 1 2
1 2 1
2 1 1

${}^6{C}_1{\times }^3{C}_1\times {}^4{C}_2+{}^6{C}_1\times {}^3{C}_2\times 4C_1+{}^6{C}_2\times {}^3{C}_1\times {}^4{C}_1$
$=108+72+180=360$