Question

The number of $6$ digits numbers that can be formed using the digits $1,3,5$ so that $5$ occurs twice in each number is

• A. $260$
• B. $180$
• C. $120$
• D. $240$

Answer 1

Answer: (D)

$240$

We have to form $6$ digits numbers of which two digits must necessarily be $5$. The digit $5$ can be arranged in ${{}^{6}C}_2$ ways.

Now for the remaining $4$ places, we have two options, $1$ or $3$ in every place. Thus the remaining $4$ places can be filled in $2^4$ ways. So the required number of numbers are $2^4\times {{}^{6}C}_2=240$