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

1 Answer | Add Yours

tiburtius's profile pic

tiburtius | High School Teacher | (Level 1) Educator

Posted on

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`

We’ve answered 315,638 questions. We can answer yours, too.

Ask a question