Mike D. answered • 09/13/21

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- C(9,5) = C(9,4) as the number of ways of selecting 5 from 9 is the same as selecting 4 from 9 and then taking the other 5. C(9,5) > C (8,5) because there are more ways of selecting 5 from 9 than 5 from 8 as you start with a bigger group. So C(9,4) is the bigger. [ you can check this by calculating both on a TI-84 say]
- C (n,r) = n! / r! (n-r) ! so C(8,5) = 8! / 5! 3! = 8.7.6.5.4 / 5.4.3.2.1 = 8.7.6 / 3.2.1 = 56. 6! = 6.5.4.3.2.1 = 720, SO 6! is larger
- Same argument as 1. C (15,4) = C (15,5) > C (12,5) because 15 > 12
- Clearly 5 ! < 6! = 720 from (2) to 3535 must be larger