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11 Apr 2017, 10:51
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A men's basketball league assigns every player a two-digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g. 22), and no two players have the same number?
A. 20
B. 21
C. 22
D. 24
E. 25
A. 20
B. 21
C. 22
D. 24
E. 25
11 Apr 2017, 11:04
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Bunuel
Take the task of creating different jersey numbers and break it into stages.
Stage 1: Select the first digit
There are 5 digits (1, 2, 3, 4, or 5) to choose from, so we can complete stage 1 in 5 ways
Stage 2: Select the second digit
Repeated digits are NOT ALLOWED.
So, once we select the 1st digit in stage 1, we cannot select it again.
So, there are 4 digits remaining to choose from.
We can complete stage 2 in 4 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create the 2-digit jersey numbers) in (5)(4) ways ( = 20 ways)
Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch the following videos:
gmathopeful19
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11 Apr 2017, 11:25
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I did 5 * 5 and then subtracted the repeated digit numbers like 11.
So 25 - 5 = 20
Posted from my mobile device
I did 5 * 5 and then subtracted the repeated digit numbers like 11.
So 25 - 5 = 20
Posted from my mobile device
