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 at least one member from each of the regional groups, is

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

Answer 1

The correct option is C $360$

$\begin{array}{ccc}\text{Asians(6)}& \text{Europeans(3)}& \text{Americans(4)}\\ 1& 1& 2\\ 1& 2& 1\\ 2& 1& 1\end{array}$

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