Question

The sum of five digit numbers which can be formed with the digits $3,4,5,6,7$ using each digit only once in each arrangement is

• A. $5666600$
• B. $6666600$
• C. $7666600$
• D. None of these

Answer 1

Answer: (B)

$6666600$

The number of numbers of $5$ digits, having $3$ in unit's place = number of arrangement of the remaining $4$ digits $={{}^{4}P}_4=24$

Similarly, for other digits also, each digit occurs $24$ times in units place.

So the sum of digits in unit's place$=24\times 3+24\times 4+24\times 5+24\times 6+24\times 7=600$

Similarly, the number of digits in each of the other places$=600$

Thus the required sum$=600\times 10000+600\times 1000+600\times 100+600\times 10+600\times 1=6666600$