For choosing teams, you want to keep in mind the combination basics...

you want to choose out of n people, create a team of r. THe number of combinations (NOT permutations) should be between 21-24. That's more than 20 and less than 25.

So, if you try the various combinations the only one that works is out of 7 choose a team of 5.

THat's 7NCR5

7! / (5! 2!) = 6*7/2 = 21

What about 8C4?

8! / (4!*4!) = 5*6*7*8/4 = 30*7*2 = 240

What about 8C5?

8! / (5! 3!) = 6*7*8 / (3*2) = 56

What about 8C6?

8! / (6! 2!) = 7*8 / 2 = 28

What about 8C7?

8! / (7! 1!) = 8

So somehow we don't get in the correct range. You can try for the others but you won't get in range.

6C3 = 6! / (3! 3!) = 4*5*6 / (3*2) = 20

6C4 = 6! / (4! 2!) = 5*6 / 2 = 15

The highest number of combinations will be in the middle. So 6C3 will be the max for 6 people. 4C2 will be the max for 4 people. So if 6C3 only has 20, we know we need to go higher to 7.

7C4 = 7! / (4! 3!) = 5*6*7 / (3*2) = 5*7 = 35 (too high)

7C5 = 7! / (5! 2) = 6*7 / 2 = 21 (just right!)

So if you're familiar with the binomial distribution curve for these combinations and that out of 8 you choose a number in the middle you'll get the highest number of results. Using that you can do an educated guess as to what to try next.

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