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 .
With repeats: 8^5 = 32768 Without repeats: 8 x 7 x 6 x 5 x 4 = 6720
Without repeats, 4*3*2*1 = 24 If repeats are allowed, then 4*4*4*4 = 256
With repeats: 55 = 3125 Without repeats: 5 x 4 x 3 x 2 x 1 = 120
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.
There are 600 5-digit numbers divisible by 150.
120
With repeats: 8^5 = 32768 Without repeats: 8 x 7 x 6 x 5 x 4 = 6720
Without repeats, 4*3*2*1 = 24 If repeats are allowed, then 4*4*4*4 = 256
With repeats: 55 = 3125 Without repeats: 5 x 4 x 3 x 2 x 1 = 120
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.
There are 600 5-digit numbers divisible by 150.
There are five such numbers.
If repeats are permitted: 2 x 5 x 5 = 50 different odd numbers If repeats are not permitted: 2 x 4 x 3 = 24 different odd numbers
Assuming the question refers to changing the order of the six digits, with no digit repeating and no leading 0s, the answer is 1630 numbers. Of these 5 are of 1 digit, 25 of 2-digit and so on. If repeats are allowed, but no leading 0s then 46,655 If repeats and leading 0s are both allowed then 55987 The situation gets much more complicated if numbers can be made by other means, for example 92*4-5*60
60 different numbers can be formed from the digits {1, 2, 3, 4, 5} is no repeats are allowed Any of the first digits can be chosen for the first digit, leaving 4 for the next and 3 for the final digit. Thus there are 5 × 4 × 3 = 60 different possible such permutations of 3 digits from the 5.
With a total of 90,000 five digit numbers, we can conclude that there is 45,000 EVEN five digit numbers.
There are 9000 of them.