Question

How many numbers greater than $40000$ can be formed from the digits $2,4,5,5,7?$

• A. $12$
• B. $24$
• C. $36$
• D. $48$

Answer 1

The correct option is D

$48$

Explanation for the correct option:

Find the total numbers.

Five digits $2,4,5,5,7$ are given by which we have to find how many numbers greater than $40,000$ can be formed.
Let us make a box of five sections to understand the concept easily.

1st

2nd

3rd

4th

5th

Initially, we have to fix a digit at $1$st position and the first position can be filled by four digits out of $5$ digits (excluded $2$ ).
We can’t place $2$ at the first position because it is mandatory to form a no. greater than $40,000$and if we place $2$at first position the no. will be less than$40,000$.
So 1st position can be filled in $=4$ ways.
The rest of the positions can be filled in $={\displaystyle \frac{4!}{2!}}$ ways.
We divided the outcome by$2!$ because $5$ comes two times in the number.
So the required ways in which numbers greater than can be formed from the digits $2,4,5,5,7$ are

$=$ The number of ways the first position can be filled $\times$ the no. of ways the rest of the positions can be filled

$=4\times {\displaystyle \frac{4!}{2!}}$ways
$={\displaystyle \frac{4\times 4\times 3\times 2\times 1}{2\times 1}}$ways
$=48$ ways.
Therefore, $48$ numbers greater than $40,000$ can be formed from the digits $2,4,5,5,7$.
Hence, the correct option is D.