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The first digit can be any one of 9 (not zero). For each of those . . .
The second digit can be any one of 9. For each of those . . .
The third digit can be any one of the remaining 8. For each of those . . .
The fourth digit can be any one of the remaining 7. For each of those . . .
The fifth digit can be any one of the remaining 6.
Total number of possibilities = (9 x 9 x 8 x 7 x 6) = 27,216 .
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How many 5 digit numbers can be formed by the digits 1 through 8?
With repeats: 8^5 = 32768 Without repeats: 8 x 7 x 6 x 5 x 4 = 6720
How many 4-digit numbers can be formed using the numbers 5 6 7 and 8?
Without repeats, 4*3*2*1 = 24 If repeats are allowed, then 4*4*4*4 = 256
How many positive integers less than 100 can be written using the digits 3 and 4 and 5 and 6?
If two digit number can have a repeated digit (eg 44) then there are 20 possible numbers, otherwise there are 16 possible numbers: There are 4 single digit numbers; With repeats allowed there are a further 4 x 4 = 16 two digit numbers making a total of 20; Without repeats allowed there are a further 4 x 3 = 12 two digit numbers making a total of 16.
How many five digit numbers can be made using the digits 1 2 3 4 5?
With repeats: 55 = 3125 Without repeats: 5 x 4 x 3 x 2 x 1 = 120
How many 5 digit numbers are divisible by 150?
There are 600 5-digit numbers divisible by 150.
