# Three cards are drawn at random from a pack of cards, without replacement. find the probability that at least two of them are aces.?

thanks in advance

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- cidyahLv 75 years agoBest Answer
Three cards may be drawn from a deck in 52C3 = 22,100 ways.

P(at least 2 aces ) = P( 2 ace , 1 non-aces) + P( 3 aces , 0 non-aces)

There are 4 aces and 2 may be drawn in 4C2=6 ways and 1 non-ace may be drawn from the remaining cards in 48C1 = 48 ways.

P( 2 ace, 1 non-aces) = (4C2)(48C1) /52C3 = (6)(48 ) / 22100 = 288 /22100

Three aces may be drawn in 4C3 = 4 ways

P( 3 aces ) = (4C3)(48C0) / 52C3 = 4 / 22100

P( at least 2 aces) = 288/22100 + 4/22100 = 292 / 22100

- M3Lv 75 years ago
indicated Pr = P(3aces) + P(2aces & 1 non-ace)

= (4c3 + 4c2*48c1)/52c3 = (4+288)/22100

= 73/5525, ≈ 1.32%

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