Permutation/Combinations

Question

A men's basketball league assigns every player a two digit number for the back of his jersey. If the league uses only digit 1-5, what's the maximum number of players that can join the league such that no player has a number with a repeated digits, and no two players have the same number?

I understand the logic behind this which is for the first digit there are 5 choices and for the second one there are 4 choices so the total number of choices would be 5*4=20 BUT the question is asking how many players NOT how many choices, so when each player receives a different 2 digit number then the total number of players receiving 2 different digit numbers should be 20/2=10 players, but the answer here is 20, and I'm wondering why? can anyone please explain? thank you

aaggar7 · Answer

Hi Madimo,

1st digit( ten's digit ) can be any one from 1 to 5.
2nd digit (unit's digit ) can be from 1 to 5.

So total combinations possible are = 5 * 5 = 25
I hope you understood the explanation till this step.

Now same digit numbers are to be subtracted i.e (11,22,33,44,55).5 such numbers are possible.

So 25 - 5 = 20 (Answer)

Please thank if you find my response useful.

Brent@GMATPrepNow · Answer

madimo11 wrote:A men's basketball league assigns every player a two digit number for the back of his jersey. If the league uses only digit 1-5, what's the maximum number of players that can join the league such that no player has a number with a repeated digits, and no two players have the same number?

I understand the logic behind this which is for the first digit there are 5 choices and for the second one there are 4 choices so the total number of choices would be 5*4=20 BUT the question is asking how many players NOT how many choices, so when each player receives a different 2 digit number then the total number of players receiving 2 different digit numbers should be 20/2=10 players, but the answer here is 20, and I'm wondering why? can anyone please explain? thank you

I highlighted what I believe to be the problem.
Are you assuming that each player receives 2 different 2-digit numbers? In other words, each player receives 2 jerseys and the 2 jerseys have different numbers? If that were the case, we'd need to divide the 20 possible jerseys by 2 to get 10 (as you suggest).
However, the original question does not say that each player receives 2 jerseys.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Brent@GMATPrepNow · Answer

I should mention that, when the answer choices are relatively small, it's not a bad idea to consider listing the possibilities.
Here, the jersey possibilities are:
12, 13, 14, 15, 21, 23, 24, 25, 31, 32, 34, 35, 41, 42, 43, 45, 51, 52, 53, and 54

There are 20 in total.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Scott@TargetTestPrep · Answer

madimo11 wrote:A men's basketball league assigns every player a two digit number for the back of his jersey. If the league uses only digit 1-5, what's the maximum number of players that can join the league such that no player has a number with a repeated digits, and no two players have the same number?

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.

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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