Asked by Kassie

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?
Answered by Reiny
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
Answered by Kassie
I'm confused as to how you're getting these numbers... Could you possible break it down a little farther please? I don't understand how you get from C(52,5)=2598960...Thank you so much for helping!
Answered by Reiny
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
<sub>n</sub>C<sub>r</sub>

so enter
13
2nd F
<sub>n</sub>C<sub>r</sub>
5
=

You should get 1287
Answered by Asnake
253/9996
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