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I am trying to find a formula to give me the number of permutations of 3 numbers across multiple sets of numbers. For example I have 5 different sets call them a,b,c,d,e with numbers 1-10 and I want to know if we use one number from each how many permutations of just 3 there are across these sets ie a1, d3, e2.

There can only be one number per letter - no combinations of say a1,a2,b3.

The letters must follow in order ie c cannot come before b.

I am interested to see the formula itself so that the number of sets can be increased as necessary but I am only interested in permutations of 3.

Many thanks,

Gordon

Gordon
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  • Are the subsets $a_1,d_3,e_2$ and $b_1,d_3,e_2$ identical as far as you're concerned? If not (i.e., they are considered different), then simply choose $3$ out of $5$ sets, and then choose $1$ out of $10$ numbers from each set. So the number of combinations is $\binom53\cdot10^3$. – barak manos Sep 10 '15 at 08:59
  • Thank you for your comment Barak, I would consider them to be different. I am not that clued up on entering formulas so how would yours be entered on a calculator and what result would it give ? – Gordon Sep 10 '15 at 11:49
  • $\binom53\cdot10^3=\frac{5!}{3!\cdot2!}\cdot1000=10000$. – barak manos Sep 10 '15 at 12:06
  • So if I follow correctly that would make 120,000 combinations if we looked for the same size of subsets 3 from 10 sets ? – Gordon Sep 10 '15 at 12:24
  • Looks like it... – barak manos Sep 10 '15 at 12:35
  • You're a gentleman - thank you very much – Gordon Sep 10 '15 at 12:43

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