Question

Find the sum of all $4-$digit numbers that can be formed using the digit $1,3,5,7,9$

Answer 1

Total no. of digits are $5$, i.e.,

$n=5$

Total no. of digits required is $4$, i.e.,

$r=4$

Therefore,

No. of $4$ digits no. that can be formed $={}^n{P}_r={}^5{P}_4=\frac{5!}{1!}=120$

No. of times each digit will appear $=\frac{120}{5}=24$

Sum of digits at unit place $=24(1+3+5+7+9)=24\times 25=600$

Sum of all numbers $=600\times 1000+600\times 100+600\times 10+600=666600$

Hence the sum off all $4$ diit numbers is $666600$.