5,678
How Many 5 Digit Numbers Can Be Formed With The Below Digits?
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.