Cards Deck
If three cards are successively dealt from a 52-card deck?
Math problem:
If three cards are successively dealt from a 52-card deck without replacement, in how many ways could they be a face card, then a spade, and then a heart?
12 face cards, among which are 3 spades and 3 hearts (coz aces ain't faces to me).
13 spades, and
13 hearts.
P(a face card, then a spade, and then a heart)
= [6C1*(13C1)^2 + 2(3C1)(12C1)(13C1)] / 52C3
= [6*13^2 + 2*3*12*13] / 52C3
= 6*13*(13+12) * 1*2*3 / 50*51*52
= 9*13*100 / 50*51*52
= 3 / 34
ah, sorry! you asked for some other thing, not the probability.
ways
= [6*13^2 + 2*3*12*13]
= 1950
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