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| Math Central | Quandaries & Queries |
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Question from CC, a student: You have a license plate it can have 6 numbers/letters you can use the numerals 0-9 and the letters A-Z how many combos are possible and how did you figure it out? Question 2, Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards. Need to know how you come to the answer as well. |
CC,
For your first problem you have 6 places to fill and for each place you have 36 choices for the entry, 26 letters and 10 digits. Thus in total you have 36 × 36 × 36 × 36 × 36 × 36 = 366 possible license plates.
Question 2,
If you want to count the number of ways to choose 3 of the 4 possible kings it's easier to think of the king you don't choose. There are 4 ways to choose which king not to include so there are 4 ways to choose 3 kings from 4 kings.
Now count the number of ways of choosing 2 queens from 4 queens.
If you start with the queen of spades there are 3 ways to choose the second queen.
If you start with the queen of hearts there are 3 ways to choose the second queen.
If you start with the queen of diamonds there are 3 ways to choose the second queen.
If you start with the queen of clubs there are 3 ways to choose the second queen.
Thus we have counted 4 × 3 ways to choose 2 queens. But we have counted each combination twice for example we counted the queen of spades first and the queen of hearts second and also the queen of hearts first and the queen of spades second. Hence the number of ways of choosing 2 things (queens) from 4 things is (4 × 3)/2. Hence the number of KKKQQ hands is 4 × (4 × 3)/2.
Harley
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