Peter is picking a number for his jersey. He wants to have a 2-digit number with an odd digit in the tens-place and an even digit in the ones-place. How many different choices does Peter have?
* This problem is a permutation and combination.
Peter wants an odd digit in the tens place. The numbers eligible are: 1, 3, 5, 7, 9 (5 digits)
He also wants an even digit in the ones-place. The numbers eligible are: 0, 2, 4, 6, 8 (5 digits)
To start off let us pretend that Peter chooses 1 as his tens place digit. What are all of the different possibilities for his jersey number? He can have 10, 12, 14, 16, or 18. This gives peter 5 different options that all have 1 in the tens place.
Now let us pretend Peter chooses 3 as his tens digit. Once again he has 5 different options for his jersey number - 30, 32, 34, 36, and 38.
Note that for every single tens place digit that Peter chooses, he will have 5 different options for the ones digit.
Since there are 5 different options for the tens digit and each of those 5 options has 5 possibilities for the ones digit. Peter has 5x5 = 25 options total. See the image below for more clarification on why we are multiplying 5x5.
Answer = Peter has 25 different choices
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