Question

The number of five digit number that can be formed by using $1,2,3$only ,such that exactly three digit of the formed numbers are same is ?

• A. $30$
• B. $60$
• C. $90$
• D. $120$

Answer 1

The correct option is B

$60$

Explanation for the correct option:

Finding the number digits formed:

Given $1,2,3$numbers.

The number which is repeated thrice can be chosen in $3$ ways {from $1,2,3$}

The number $aaabc$ can be rearranged is given by

$\frac{\text{No. of ways}}{\text{Total no. of digits}}=\frac{5!}{3!}$
$=20$ ways

Similarly for the other numbers, $3\times 20=60$ such numbers.

Hence the correct answer is option (B).