Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time.

Explanation

No. of ways to place given 4 digits at 4 places `= .^(4)P_(4) = lfloor4 = 24`
`:.` Each digit comes `lfloor3 = 6` times at unit place.
`rArr` Sum of digit at unit place `= (2+3+4+5) xx 6 = 84`
Again each digit will come `lfloor3 = 6` times at tens, 100th and 1000th place
`:.` Sum of digits at 10th, 100th and 1000th place `= (2+3+4+5) xx 6 = 84`
and the sum of all 24 numbers
`= 84 xx 1000 +84 xx 100 +84 xx 10 +84`
`= 84000 + 8400 + 840 +84 = 93324`.