5,678

Total number = 1, 2, 3, 4, 5, 6, 7, 8 = 8

First place can be filled in = 8 ways. (1,2,3,4,5,6,7,8)

Second place can be filled in = 7 ways. (one number is selected for the first place so left with 7 numbers for the second place)

Third place can be filled in = 6 ways. (two numbers are selected for the 1st and 2nd place so left with 6 numbers for the 3rd place)

Fourth place can be filled in = 5 ways. (three numbers are selected for the 1st,2nd and 3rd place so left with 5 numbers for the 4th place place)

Fifth place can be filled in = 4 ways. (four numbers are selected for the 1st ,2nd, 3rd and 4th place so left with 4 numbers for the 5th place).

Total 2 digit numbers= 8x7 = 56.

Total 3 digit numbers= 8x7x6 = 336.

Total 4 digit numbers= 8x7x6x5 = 1680.

Total 5 digit numbers= 8x7x6x5x4 = 6720. >>answer

First place can be filled in = 8 ways. (1,2,3,4,5,6,7,8)

Second place can be filled in = 7 ways. (one number is selected for the first place so left with 7 numbers for the second place)

Third place can be filled in = 6 ways. (two numbers are selected for the 1st and 2nd place so left with 6 numbers for the 3rd place)

Fourth place can be filled in = 5 ways. (three numbers are selected for the 1st,2nd and 3rd place so left with 5 numbers for the 4th place place)

Fifth place can be filled in = 4 ways. (four numbers are selected for the 1st ,2nd, 3rd and 4th place so left with 4 numbers for the 5th place).

Total 2 digit numbers= 8x7 = 56.

Total 3 digit numbers= 8x7x6 = 336.

Total 4 digit numbers= 8x7x6x5 = 1680.

Total 5 digit numbers= 8x7x6x5x4 = 6720. >>answer

24

34

This is the number of permutations of 8 things taken 5 at a time.

P[8,5] = 8!/(8-5)! = 8*7*6*5*4 = 6720 as Ellie82 says.

P[8,5] = 8!/(8-5)! = 8*7*6*5*4 = 6720 as Ellie82 says.