1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Counting Techniques Question: Drawing 5 specific cards out of a deck

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    We draw 5 cards out of a normal deck of 52 cards. No replacements.
    How many combinations have exactly one Jack, one Queen, one King?

    2. Relevant equations

    3. The attempt at a solution

    The solution = 49,920

    My attempts:

    I keep getting 99,840.

    So 4C1 Jack, 4C1 Queen, 4C1 King, then for remaining two cards 40 possible, then 39 possible.

    I go 4C1 x 4C1 x 4C1 x 40 x 39 = 99,840

    Are there combinations that are repeated somewhere then? :S
  2. jcsd
  3. Mar 31, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    After choosing 1 Jack, 1 Queen and 1 King you need to choose two more cards from 40. The number of ways of doing that =?

  4. Mar 31, 2012 #3
    oh! thanks Ray! Why doesn't it work going 40 x 39 instead of 40C2? Does 40 x 39 not work because that takes into account order as being relevant?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook