Permutation/Combinations

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madimo11: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Nov 12, 2012 11:20 am

by madimo11 » Sun Jun 09, 2013 7:15 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Jun 09, 2013 7:15 pm

aaggar7: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 11, 2012 8:48 pmFollowed by: 1 member; Thanked: 9 times

by aaggar7 » Mon Jun 10, 2013 5:22 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 10, 2013 7:11 am

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 10, 2013 7:14 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8212; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Dec 13, 2017 3:51 pm

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.

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