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 Question from david, a parent: how many combinations of 6 numbers can there be using 12 different numbers without using the same numbers more than once?× 2, 3, 5, 8, 9, 11, 12, 14, 17, 19, 20 & 31.

David,

I am going to assume that order matters, that is 2,3,5 is distinct from 2,5,3. Mathematicians call these permutations.

How many permutations of one number can there be using 12 different numbers without using the same numbers more than once?

There are 12 numbers to choose from so the answer is 12.

How many permutations of two numbers can there be using 12 different numbers without using the same numbers more than once?

Each of the 12, one number permutations above can be extended to a two number permutation by using any of the 11 numbers remaining. Thus the answer is 12 × 11 = 132.

How many permutations of three numbers can there be using 12 different numbers without using the same numbers more than once?

Each of the 132, two number permutations above can be extended to a three number permutation by using any of the 10 numbers remaining. Thus the answer is 12 × 11 × 10 = 1320.

How many permutations of four numbers can there be using 12 different numbers without using the same numbers more than once?

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If order is not important write back and I'll show you how to modify this technique,
Penny

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