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My statistics aren't too great, so I'm struggle to work out the result of the following situation.

Say you have 5 sets of 5 possible options (25 options total); and you select 1 option from each set. Each time you select 1 option from a set, that set is removed from the next round of possible options; leaving 4 sets of 5 possible options. Again, pick another option, leaving 3 sets of 5 possible options.

So the selection process is to pick 5 options, one from each set; and the total amount of options reduces by 5 on each round of selection.

Eg.

Set 1
Option 1, Option 2, Option 3, Option 4, Option 5

Set 2
Option 6, Option 7, Option 8, Option 9, Option 10

Set 3
Option 11, Option 12, Option 13, Option 14, Option 15

Set 4
Option 16, Option 17, Option 18, Option 19, Option 20

Set 5
Option 21, Option 22, Option 23, Option 24, Option 25
  1. So you pick Option 1 first, that leaves Sets 2-5 (20 options remaining)
  2. Then you pick Option 6, that leaves Sets 3-5 (15 options remaining)
  3. You pick Option 11, that leaves Sets 4-5 (10 options remaining)
  4. You pick Option 16, that leaves Set 5 (5 options remaining)
  5. You pick Option 21, there are no items left

The order that the items are selected in is not important - but how many possible combinations does it mean you could select?

The very basic maths of 

25 * 20 * 15 * 10 * 5 = 375,000

Wouldn't factor in out-of-order repetition (which we don't care about).

So how many combinations could there be?

Ben Lessani
  • 123

1 Answers1

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You don't need to worry about the person choosing from the second set first, then the first, since in the end, there is exactly one option chosen from each set. Thus you can view the choices being made in order: first one option is chosen from 1-5, then one in 6-10, and so on, so that you get $5^5=3125$ possibilities.

Mario Carneiro
  • 27,438