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Q: What are the 5-number combinations not using any number twice?

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36324

There are 360 of them.

There is 1 combination of all ten numbers, 10 combinations of one number and of nine numbers, 45 combinations of two or eight numbers, 120 combinations of three or seven numbers, 210 combinations of four or six numbers and 252 combinations of five numbers. That is 1023 = 210 - 1 in total.

128

There are 120 permutations and 5 combinations.

Assuming you are using the standard English alphabet, the number of combinations you can make are: 26 x 26 = 676 combinations.

The order of the digits in a combination does not matter. So 123 is the same as 132 or 312 etc. There are 10 combinations using just one of the digits (3 times). There are 90 combinations using 2 digits (1 once and 1 twice). There are 120 combinations using three different digit. 220 in all.

9000

This is a factorial problem. The first number can be any of ten digits, the second any of nine (because you can't repeat a digit), the third any of eight and the fourth any of the remaining 7 digits. 10x9x8x7=5040 combinations.

98765

The answer is 31C5 = 31!/[26!5!] = 169,911

10,000 combinations.

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