Question

How many numbers greater than 1000 can be formed from the digits 1, 1, 2, 2, 3 ?

Answer 1

Any $4$ or $5$ digits number formed by using the digits $1,1,2,2,3$ will be greater than $1000.$
Now consider the four digits number with only two repeating digits.
1) $1123$ no. of numbers with these digits will be $\frac{4!}{2!}=12$ ... $\left(i\right)$
2) $2213$ no. of numbers with these digits will be $\frac{4!}{2!}=12$ ... $\left(ii\right)$
Now, consider the numbers with 2 repeating digits.
$1122$... no of numbers with these digits will be $\frac{4!}{2!2!}=6$ ...(iii)
Now the five digit numbers will be
$=\frac{5!}{2!.2!}=30$.
Hence the required number of numbers will be
$=12+12+6+30$
$=60$