Question

Find the sum of all the numbers that can be formed by taking all the digits at a time from $4,5,6,7,8$ without repetition.

• A. $133320$
• B. $244420$
• C. $7999920$
• D. $2233440$

Answer 1

Answer: (C)

$7999920$

Given numbers $4,5,6,7,8$

Total possible numbers $=5!=120.$

Since all numbers are taken at a time they form $5$ digit number.

$\Rightarrow$ Each number appears $\frac{120}{5}=24$ times in each place (units, tens....)

$\Rightarrow$ Sum $=10000(4+5+6+7+8)24+1000(4+5+6+7+8)\times 24+100(4+5+6+7+8)24+$

$10(4+5+6+7+8)24+1\times (4+5+6+7+8)24$

$=11111\left(30\right)24$

$=7999920$