Em A.

asked • 06/08/15

help with algebra: 4 letters, without replacement, from 17 distinct letters

How many ways are there of choosing
4 letters, without replacement, from 17
distinct letters,
if the order of the choices is relevant?
if the order of the choices is not relevant

1 Expert Answer


Maria E. answered • 06/08/15

5 (11)

Certified Elementary Teacher - Loves Math!

Stephanie M.

You've mixed up your permutations and combinations. In (A), you've actually described a situation where the order is relevant. That's because 17x16x15x14 counts, say, both ABCD and DCBA. I could draw A first (one of the 17 letters), then B (one of the 16 remaining letters), then C, then D. Or, I could draw D first (another one of the 17 letters), then C (one of the remaining 16 letters), then B, then A.
So, there are 17x16x15x14 = 57120 ways to chose if the order is relevant.
To get from there to a situation in which the order isn't relevant, you should actually divide by 4x3x2x1 (the number of ways to arrange the four letters), not multiply as you suggest in (B). So, there are 57120/(4x3x2x1) = 57120/24 = 2380 ways to choose if the order isn't relevant.


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