# There are three football jerseys in a laundry hamper, with the numbers 18, 88, and 93 on the back, respectively. A total of three selections are made from the hamper, each time noting the number on...

There are three football jerseys in a laundry hamper, with the numbers 18, 88, and 93 on the back, respectively. A total of three selections are made from the hamper, each time noting the number on the back of the selected jersey. If the number 18 jersey is selected on any reach into the hamper, it is returned before the next selection. Otherwise, the selected jersey is not replaced before the next reach into the hamper. How many different outcomes are possible?

embizze | Certified Educator

Use a tree diagram to list the possibilities:

On the first round there are 3 possibilities -- 1 for each jersey.

On the second round there are 7 possibilities. If 18 was chosen in the first round, there are 3 possibilities in the second round.

If 88 was chosen in the first round, then there are only two choices in the second round as 88 was not replaced and simarly 2 choices if 93 was chosen in the first round.

On the third round there are 13 possibilities.

18->18->3 choices
18->88->2choices
18->93->2choices
88->18->2choices
88->93->1choice
93->18->2choices
93->88->1choice
13 choices

Thus there are 13 different outcomes.

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Let A=18,B=88,C=93 . We are looking for the number of 3 letter combinations where B and C do not repeat but A is allowed to repeat.

There are 27 total permutations -- take away 1 for all B's, 1 for all C's, 6 for 2B's and 6 for 2C's leaving 13.

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