Question

The figures $4,5,6,7,8$ are written in every possible order. The number of numbers greater than $56000$is ?

• A. $72$
• B. $96$
• C. $90$
• D. $98$

Answer 1

The correct option is C

$90$

Explanation for the correct option

Total $5$digits are given as $4,5,6,7,8.$

Let us say the number starts with $56$. Then there are three numbers left that can be arranged in $3!$ways

$3!=6$

The numbers starting with $57$ and $58.$

So, $3\times 6=18$ numbers.

The number that starts with $6$, then

Number of ways $4$ digits can be arranged $=4\times 3\times 2\times 1=24$

In the same way, for $7$and$8,$ we get$24$ for each.

Therefore, total number of numbers greater than $56000$ will be

$$\begin{gathered} =(24\times 3)+18 \\ =72+18 \\ =90 \end{gathered}$$

Hence, option C is correct.