In how many ways can 50 cards be chosen from a standard deck of 52 cards?

1 answer:

7 0

The answer must take into account that the order is irrelevant, that is that it is the same J, Q, K that Q, K, J, and K, J, Q and all the variations of those the three cards.

The number of ways you can draw 50 cards from 52 is 52*51*50*49*48*47*...4*3 (it ends in 3).
,
But the number of ways that those 50 cards form the same set repeats is 50! = 50*49*49*47*....3*2*1

So, the answer is (52*51*50*49*48*....*3) / (50*49*48*...*3*2*1) = (52*51) / 2 = 1,326.

Note that you obtain that same result when you use the formula for combinations of 50 cards taken from a set of 52 cards:

C(52,50) = 52! / [(50)! (52-50)!] = (52*51*50!) / [50! * 2!] = (52*51) / (2) = 1,326.

Answer: 1,326

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