How many different 4-digit number can be formed with the digits 1,2,3,4 without any repetition ? Also find their sum.

Explanation

Problem reduces to filling up 4 blank spaces. Th, H, T and U or unit places which indicate respectively the thousand, hundred, ten and unit place. Th place can be filled by any one 1, 2,3,4 in 4 different ways. Then three digits remain after filling up H in any way. So H can be filled in 3 ways and so on.
Th ,H ,T ,U
Hence , total number of 4 digit number `=4xx3xx2xx1=4!""=24`
For finding sum of these 24 numbers let us write numbers , one below another, putting elements of U,T,H,Th in same vertical columns. We find that in each column each of digits 1,2,3,4 occurs `24 div 4=6` times. Hence , sum of the digits in each column `=6xx(1+2+3+4)=60`
`therefore ` Total sum required `=(60(10^(3)+10^(2)+10+1)`
`=60xx1111=66660`