Question

Find the sum of all 5 digits numbers that can be formed by using the digits 1,3,4,5,7 if repetition of digits is not allowed

Answer 1

The different numbers that can be formed using these numbers are total 5! = 120 numbers
Now when unit digit is fixed then others can be arranged in 4! =24 ways
Thus all numbers out of ( 1,3,4,5,7 ) will repeat 24 times forming unit digits of 120 numbers
Similarly for other place digits each of these 5 numbers will be repeated 24 times
$$\begin{gathered} \mathrm{Thus}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{unit}\mathrm{digits}=24\times 7+24\times 5+24\times 4+24\times 3+24\times 1=480 \\ \mathrm{Thus}\mathrm{sum}\mathrm{of}\mathrm{all}5\mathrm{digit}\mathrm{numbers}=480\times 1+480\times 10+480\times 100+480\times 1000+480\times 10000=5333280 \end{gathered}$$