The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2, and 3 is a. `26664` b. `39996` c. `38664` d. none of these

Options

A. 26664
B. 39996
C. 38664
D. none of these

Explanation

We have,
Required sum
= Sum of all the numbers formed by the digits 0, 1, 2, 3
- Sum of all the numbres having 0 at thousand place
`=(0+1+2+3)xx(4-1)!((10^(4)-1)/(10-1))`
`-(1+2+3)(3-1)!((10^(3)-1)/(10-1))`
`=6xx3!xx((10^(4)-1)/(9))-6xx2!xx((10^(3)-1)/(9))`
`=4(10^(4)-1)-(4)/(3)xx999=40000-4-1332=38664`.
ALITER We have,
Number of numbers with 0 in the unit's place = 3!=6
Number of numbers with 1 or 2 or 3 in the units place `3!-2!=4`.
`:.` Sum of the digit in unit's place
`=6xx0+4xx1+4xx2+4xx3=24`.