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What is theoretical probability of being dealt exactly two 8's in a 5 -card hand from a...

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connorcolin3 | Valedictorian

Posted March 21, 2013 at 8:14 PM via web

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What is theoretical probability of being dealt exactly two 8's in a 5 -card hand from a  standard 52 card deck?

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted March 21, 2013 at 8:34 PM (Answer #1)

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We can deal two 8's in `((5),(2))=10` ways. So we have dealt two 8's and there are 48 cards remaining from which we need to choose 3 (48 because we musn't choose another 8 so 52 cards - 4 8's = 48) which we can do in `((48),(3))=17296` ways.

Also total number of all 5-card combinations we can deal from deck of 52 cards is `((52),(5))=2598960`.

So probability of being dealt exactly two 8's in a 5-card hand from a standard 52 card deck is   `P=(((5),(2))((48),(3)))/(((52),(5)))=(10cdot17296)/2598960approx0.0665497`

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