# A bag contains six white marbles and five red marbles.Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour

$\begin{array}{1 1}(A)\;10\\(B)\;15\\(C)\;20\\(D)\;25\end{array}$

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• $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Total no of white marbles =6
Total no of red marbles =5
The no of ways of which all are white marbles =$6C_4$
All are red marbles =$5C_4$
Total no of ways =$6C_4+5C_4$
$6C_4=\large\frac{6!}{4!2!}$
$\Rightarrow \large\frac{6\times 5\times 4!}{2\times 1\times 4!}$
$\Rightarrow 15$
$5C_4=\large\frac{5!}{4!1!}$
$\Rightarrow \large\frac{5\times 4!}{1\times 4!}$
$\Rightarrow 5$
Total no of ways =15+5=20
Hence (C) is the correct answer.