BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Tricky counting: 5-on-5 soccer game

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Tricky counting: 5-on-5 soccer game

by Brent@GMATPrepNow » Sun Sep 18, 2011 7:12 am
In response to knight247's request at https://www.beatthegmat.com/counting-met ... 87-15.html, I created this tricky counting question.

Please note that I believe that this question is beyond the scope of the GMAT.

In a 5-on-5 soccer game, the team consisting of Al, Bob, Carl, Don and Ed scored a total of 6 goals.
In how many different ways could the 6 goals have been distributed among the 5 players?

A) 30
B) 90
C) 120
D) 150
E) 210

OA: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 57
Joined: Fri Apr 09, 2010 11:54 am
Location: India
Thanked: 8 times
GMAT Score:640

by chetansharma » Sun Sep 18, 2011 7:27 am
Brent@GMATPrepNow wrote:In response to knight247's request at https://www.beatthegmat.com/counting-met ... 87-15.html, I created this tricky counting question.

Please note that I believe that this question is beyond the scope of the GMAT.

In a 5-on-5 soccer game, the team consisting of Al, Bob, Carl, Don and Ed scored a total of 6 goals.
In how many different ways could the 6 goals have been distributed among the 5 players?

A) 30
B) 90
C) 120
D) 150
E) 210

OA: E



Cheers,
Brent
Hi,

The solution for these kind of questions can be obtained using the formula (n+r-1)C(r-1), where n represents the identical items to be distributed among r people including 0. The given problem can be solved using the given formula. So the solution will be (5+6-1)C(5-1) = 10C4 which gives the answer as 210 i.e., option E

Regards,
Chetan
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Sun Sep 18, 2011 8:31 am
Thanks for that Brent. Appreciate it.

Since I'm still figuring out the problem, I thought I'd use the method I normally use to solve this problem. I've used the 'how many numbers less than 100,000 are there whose sum equals six' logic here.

The goals could be scored in the following manner
0 0 0 0 6 which can be arranged in 5 ways
0 0 0 1 5 which can be arranged in 20 ways
0 0 1 1 4 which can be arranged in 30 ways
0 0 0 2 4 which can be arranged in 20 ways
0 1 1 1 3 which can be arranged in 20 ways
0 0 1 2 3 which can be arranged in 60 ways
0 0 0 3 3 which can be arranged in 10 ways
0 0 2 2 2 which can be arranged in 10 ways
0 1 1 2 2 which can be arranged in 30 ways
1 1 1 2 2 which can be arranged in 5 ways

Sum=210 ways. Hence E
Last edited by knight247 on Sun Sep 18, 2011 2:09 pm, edited 1 time in total.
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Sun Sep 18, 2011 8:36 am
@Chetan...Great stuff with the formula bro. How did you come up with that? or did you get it from some source?
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 18, 2011 9:05 am
chetansharma wrote: The solution for these kind of questions can be obtained using the formula (n+r-1)C(r-1), where n represents the identical items to be distributed among r people including 0. The given problem can be solved using the given formula. So the solution will be (5+6-1)C(5-1) = 10C4 which gives the answer as 210 i.e., option E

Regards,
Chetan
Exactly!
Great work, Chetan.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 57
Joined: Fri Apr 09, 2010 11:54 am
Location: India
Thanked: 8 times
GMAT Score:640

by chetansharma » Sun Sep 18, 2011 10:17 am
Thanks Brent and Knight247!!!

@Knight247, I have learned the basics of the topic in my 12th standard. Also you can get the formulae and other basics of P&C from the book "Quantitative Aptitude for CAT" by Arun Sharma.

Regards,
Chetan
Top
Legendary Member
Posts: 608
Joined: Sun Jun 19, 2011 11:16 am
Thanked: 37 times
Followed by:8 members

by saketk » Mon Sep 19, 2011 9:52 am
Hey Guys -- you can refer to the following formulas for "Restricted Permutation"


(a) Number of permutations of 'n' things, taken 'r' at a time, when a particular thing is to be always included in each arrangement

= r n-1 Pr-1

(b) Number of permutations of 'n' things, taken 'r' at a time, when a particular thing is fixed: = n-1 Pr-1

(c) Number of permutations of 'n' things, taken 'r' at a time, when a particular thing is never taken: = n-1 Pr.

(d) Number of permutations of 'n' things, taken 'r' at a time, when 'm' specified things always come together = m! x ( n-m+1) !

(e) Number of permutations of 'n' things, taken all at a time, when 'm' specified things always come together = n ! - [ m! x (n-m+1)! ]


EDIT-- added a jpeg for better readability :)
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 296
Joined: Sun May 29, 2011 5:10 am
Location: Vietnam
Thanked: 10 times
Followed by:5 members

by tuanquang269 » Wed Sep 21, 2011 7:00 pm
Brent@GMATPrepNow wrote:
In a 5-on-5 soccer game, the team consisting of Al, Bob, Carl, Don and Ed scored a total of 6 goals.
In how many different ways could the 6 goals have been distributed among the 5 players?

A) 30
B) 90
C) 120
D) 150
E) 210

OA: E

Cheers,
Brent
Now, I'll approach in this way, 6 goals will "choose" person in the set (A,B, C,D,E)
For example:

A => B B => C => D => E

It means 1st goal choose A, 2nd don't like A move "=>" to B, 3rd choose B, 4th move "=>" and choose C, 5th move and choose E

Another one is

=> => => => E E E E E E (all of 6 goals don't like the four first player and move "=>" to choose E)

So, we have number of combination of "=>" and "players" are [spoiler]10C4 = 210[/spoiler]

IMO, correct answer is E
Top
Post new topic Post Reply
• Page 1 of 1