Question

Exercise 3.8.18: How many ways are there to choose five cards from 52 so that you have all the aces? How many ways are there to choose five cards from 52 so that you have four cards with the same number?

Answer #1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

3.8.18. Total number of cards = 52

Number of ways to select five cards from 52 so that you have all the aces = Number of ways to select 4 aces from 4 x Number of ways to select 1 card from remaining 48

= 4C4 x 48C1

= 1 x 48

= **48**

Number of ways to choose five cards from 52 so that you have four cards with the same number = Number of different numbers x Number of ways to select 4 same numbers x Number of ways to select any other number

= 13 x 4C4 x 48C1

= 13 x 1 x 48

= **624**

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