Posted by **Kassie** on Tuesday, April 6, 2010 at 10:02pm.

Five cards are drawn at random without replacement from and ordinary deck of 52. What is the probability all 5 cards are from the same suit?

- Statistics -
**Reiny**, Tuesday, April 6, 2010 at 10:23pm
1 of the 4 suits ---> C(4,1) = 4

5 from one of those suits = C(13,5) ---> 1287

5 from the whole deck ---> C(52,5) = 2598960

so prob = 4(1287)/2598960

= 33/16660 = .00198

- Statistics -
**Kassie**, Tuesday, April 6, 2010 at 10:39pm
I'm confused as to how you're getting these numbers... Could you possible break it down a little farther please? I dont understand how you get from C(52,5)=2598960...Thank you so much for helping!

- Statistics -
**Reiny**, Tuesday, April 6, 2010 at 11:24pm
Have you learned the difference between permutations and combinations?

in combinations the order does not matter.

(if I hold 5 cards in my hand, the order in which they were dealt to me does not matter)

C(13,5) means ..

how many groups of 5 can I form from 13

It is short form for 13!/(5!8!)

= 13x12x11x10x...x2x1/(8x7x6x..x2x1)(5x4x3x2x1))

= 13x12x11x10x9/(5x4x3x2x1) = 154440/120 = 1287

On your calculator there is a button labeled

_{n}C_{r}

so enter

13

2nd F

_{n}C_{r}

5

=

You should get 1287

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