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A men's basketball league assigns every player a two-digit number for

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A men's basketball league assigns every player a two-digit number for [#permalink]

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New post 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

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Re: A men's basketball league assigns every player a two-digit number for [#permalink]

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New post 11 Apr 2017, 11:04
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Bunuel wrote:
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


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:




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New post 11 Apr 2017, 11:25
A?

I did 5 * 5 and then subtracted the repeated digit numbers like 11.

So 25 - 5 = 20

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Re: A men's basketball league assigns every player a two-digit number for [#permalink]

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New post 13 Apr 2017, 12:10
Since repetation is not allowed so according to simple counting method
for place 1 5 possibilities
for place 2 4 possibility
total 20
Answer is:A
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Re: A men's basketball league assigns every player a two-digit number for [#permalink]

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New post 19 Apr 2017, 16:14
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Bunuel wrote:
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


We need to determine how many two-digit numbers can be created from 5 digits (1 to 5 inclusive), and no digits can be repeated. Since order matters, we have a permutation. Thus, the number of ways to create two-digit numbers is 5P2 = 5!/(5 - 2)! = !5 x 4 = 20.

Answer: A
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Re: A men's basketball league assigns every player a two-digit number for [#permalink]

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New post 21 Apr 2017, 23:46
Bunuel wrote:
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


The question is simply asking how many unique combinations are there for a basketball player numbers- the rest of the information is superfluous

For the first number there is a pool of 5 numbers and for the second numbers there is a pool of 4 numbers
Re: A men's basketball league assigns every player a two-digit number for   [#permalink] 21 Apr 2017, 23:46
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