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52 card deck, 13 values, 4 suits 6 cards are dealt randomly. Possible outcomes? All hearts?...

52 card deck, 13 values, 4 suits 6 cards are dealt randomly.

Possible outcomes?

All hearts?

3 kings 3 aces?

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Answer #1

6 cards are dealt randomly from 52 cards.

1) Possible outcomes

= \binom{52}{6} = 20358520

2) Probability of all hearts

=\frac{\binom{13}{6}}{\binom{52}{6}} = \frac{1716}{20358520}

3)

Probability of 3 kings and 3 aces

=\frac{\binom{4}{3}\times\binom{4}{3}}{\binom{52}{6}} = \frac{16}{20358520}

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