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

Redeem

Combo.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 233
Joined: Wed Aug 22, 2007 3:51 pm
Location: New York
Thanked: 7 times
Followed by:2 members

Combo.

by yellowho » Tue Mar 01, 2011 9:54 pm
In how many ways can 6 identical coins be distributed among Alex, Bea and Chad? Note: Some people may receive zero coins.


I don't have solution to this. Is this 28?
Top
Source: — Problem Solving |
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Tue Mar 01, 2011 10:29 pm
IOM [spoiler]because some of three people (ABC) may receive zero coins, which are identical
1) A(6) B(0) C(0)
2) A(5) B(1) C(0)
3) A(5) B(0) C(1)
4) A(4) B(2) C(0)
5) A(4) B(0) C(2)
6) A(4) B(1) C(1)
7) A(3) B(3) C(0)
8) A(3) B(0) C(3)
9) A(3) B(2) C(1)
10) A(3) B(1) C(2)
11) A(2) B(4) C(0)
12) A(2) B(0) C(4)
13) A(2) B(3) C(1)
14) A(2) B(2) C(2)
15) A(2) B(1) C(3)
16) A(1) B(5) (0)
17) A(1) B(0) C(5)
18) A(1) B(1) C(4)
19) A(1) B(4) C(1)
20) A(1) B(3) C(2)
21) A(1) B(2) C(3)
22) A(0) B(6) C(0)
23) A(0) B(0) C(6)
24) A(0) B(5) C(1)
25) A(0) B(1) C(5)
26) A(0) B(4) C(2)
27) A(0) B(2) C(4)
28) A(0) B(3) C(3)

added some more and we are equal - total 28 ways



[/spoiler]
yellowho wrote:In how many ways can 6 identical coins be distributed among Alex, Bea and Chad? Note: Some people may receive zero coins.


I don't have solution to this. Is this 28?
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Tue Feb 08, 2011 8:55 pm
Location: Canada
Thanked: 7 times
GMAT Score:700

by BarryLi » Tue Mar 01, 2011 11:03 pm
[spoiler]Thank goodness the coins are identical.

For 0 coins, there is 1 combination: 0-0-0
For 1 coin, there are 3 combinations: 0-0-1, 0-1-0, 1-0-0
For 2 coins, there are 6 combinations: 0-0-2, 0-1-1, 0-2-0, 1-0-1, 1-1-0, 2-0-0

There may be a pattern of adding 1, 2, 3 to the total number of combinations, but I'll working out the case for 3 coins just to confirm this.

For 3 coins, there are 10 distributions: 0-0-3, 0-1-2, 0-2-1, 0-3-0, 1-0-2, 1-1-1, 1-2-0, 2-0-1, 2-1-0, 3-0-0

From the sequence 1, 3, 6, 10, the number of terms seems to be increasing by 2, 3, 4, etc.

0 coins: 1
1 coin: 3
2 coins: 6
3 coins: 10
4 coins: 15
5 coins: 21
6 coins: 28

Yes, the solution is 28.[/spoiler]
Top
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

by rohu27 » Tue Mar 01, 2011 11:21 pm
can we have a case here where a=b=c=0?
Night reader wrote:IOM [spoiler]because some of three people (ABC) may receive zero coins, which are identical
1) A(6) B(0) C(0)
2) A(5) B(1) C(0)
3) A(5) B(0) C(1)
4) A(4) B(2) C(0)
5) A(4) B(0) C(2)
6) A(4) B(1) C(1)
7) A(3) B(3) C(0)
8) A(3) B(0) C(3)
9) A(3) B(2) C(1)
10) A(3) B(1) C(2)
11) A(2) B(4) C(0)
12) A(2) B(0) C(4)
13) A(2) B(3) C(1)
14) A(2) B(2) C(2)
15) A(2) B(1) C(3)
16) A(1) B(5) (0)
17) A(1) B(0) C(5)
18) A(1) B(1) C(4)
19) A(1) B(4) C(1)
20) A(1) B(3) C(2)
21) A(1) B(2) C(3)
22) A(0) B(6) C(0)
23) A(0) B(0) C(6)
24) A(0) B(5) C(1)
25) A(0) B(1) C(5)
26) A(0) B(4) C(2)
27) A(0) B(2) C(4)
28) A(0) B(3) C(3)

added some more and we are equal - total 28 ways



[/spoiler]
yellowho wrote:In how many ways can 6 identical coins be distributed among Alex, Bea and Chad? Note: Some people may receive zero coins.


I don't have solution to this. Is this 28?
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Tue Mar 01, 2011 11:24 pm
I thought about this :) there's no distribution then - just 0s for everyone
rohu27 wrote:can we have a case here where a=b=c=0?
Night reader wrote:IOM [spoiler]because some of three people (ABC) may receive zero coins, which are identical
1) A(6) B(0) C(0)
2) A(5) B(1) C(0)
3) A(5) B(0) C(1)
4) A(4) B(2) C(0)
5) A(4) B(0) C(2)
6) A(4) B(1) C(1)
7) A(3) B(3) C(0)
8) A(3) B(0) C(3)
9) A(3) B(2) C(1)
10) A(3) B(1) C(2)
11) A(2) B(4) C(0)
12) A(2) B(0) C(4)
13) A(2) B(3) C(1)
14) A(2) B(2) C(2)
15) A(2) B(1) C(3)
16) A(1) B(5) (0)
17) A(1) B(0) C(5)
18) A(1) B(1) C(4)
19) A(1) B(4) C(1)
20) A(1) B(3) C(2)
21) A(1) B(2) C(3)
22) A(0) B(6) C(0)
23) A(0) B(0) C(6)
24) A(0) B(5) C(1)
25) A(0) B(1) C(5)
26) A(0) B(4) C(2)
27) A(0) B(2) C(4)
28) A(0) B(3) C(3)

added some more and we are equal - total 28 ways



[/spoiler]
yellowho wrote:In how many ways can 6 identical coins be distributed among Alex, Bea and Chad? Note: Some people may receive zero coins.


I don't have solution to this. Is this 28?
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
User avatar
Legendary Member
Posts: 543
Joined: Tue Jun 15, 2010 7:01 pm
Thanked: 147 times
Followed by:3 members

by anshumishra » Wed Mar 02, 2011 3:54 am
yellowho wrote:In how many ways can 6 identical coins be distributed among Alex, Bea and Chad? Note: Some people may receive zero coins.


I don't have solution to this. Is this 28?
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items(≤ n) is : (n+r-1)C(r-1)]

So, here the number of ways = (6+3-1)C(3-1) = 8C2 = 7*8/2 = 28.
Thanks
Anshu

(Every mistake is a lesson learned )
Top
Post new topic Post Reply
• Page 1 of 1