January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday. January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Author 
Message 
TAGS:

Hide Tags

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1199
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 09:18
Question Stats:
72% (01:34) correct 28% (02:51) wrong based on 50 sessions
HideShow timer Statistics



Manager
Joined: 16 Sep 2011
Posts: 93

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 09:54
In how many ways 10 Oranges be distributed among 2 children if both must get odd no of apples? A. 513 B. 540 C. 512 D. 515 E. 516
lets say (1,9) or (3,7) or (5,5) , (7,3) and (9,1)
so 10C1*9C9 +10C3*7C7+ 10C5*5C5+10C7*3C3+10C9*1C1 =10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10 =10+120+ 2*9*7*2+ 10*3*4 +10 =10+120+36*7+120+10 =10+120+252+120+10 =260+252=512
Option C is the answer



Manager
Joined: 04 Jun 2018
Posts: 127

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 09:58
In how many ways 10 Oranges be distributed among 2 children if both must get odd no of apples? A. 513 B. 540 C. 512 D. 515 E. 516
The children must get odd number of apples.
So If A gets 1 B can Get (3,5,7,9) Similarly we get 4 cases ie 4^4
since there are 2 children we can multiply it by 2.
So ans:256*2: 512 C



Intern
Joined: 09 Apr 2018
Posts: 17
Location: India
GPA: 3.5

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 11:58
ans is 515 9 1 10C9*9C1 7 310C7*9C3 5 510C5*9C5 3 7 1 9 add all



Manager
Joined: 05 Jul 2018
Posts: 56
Location: India
Concentration: General Management, Technology
GPA: 3.6
WE: Information Technology (Consulting)

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 20:47
Only possible number of fruits that may be given is 1,3,5,7,9 So Number of ways to select 1 fruit for 1st child & 9 fruits to second child is : 10C1*9C9 Number of ways to select 3 fruit for 1st child & 7 fruits to second child is : 10C3*7C7 Number of ways to select 5 fruit for 1st child & 5 fruits to second child is : 10C5*5C5Number of ways to select 7 fruit for 1st child & 3 fruits to second child is : 10C7*3C3Number of ways to select 9 fruit for 1st child & 1 fruits to second child is : 10C9*1C1Total = \(10C1*9C9 + 10C3*7C7 + 10C5*5C5 + 10C7*3C3 + 10C9*1C1 =10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10 =10+120+ 2*9*7*2+ 10*3*4 +10 =10+120+36*7+120+10 =10+120+252+120+10 =260+252=512\) Hence Option C is the answer
_________________
Appreciate any KUDOS given ! MY MBA RESOURCES:



Manager
Joined: 05 Jul 2018
Posts: 56
Location: India
Concentration: General Management, Technology
GPA: 3.6
WE: Information Technology (Consulting)

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
03 Nov 2018, 20:51
Only possible number of fruits that may be given is 1,3,5,7,9 So Number of ways to select 1 fruit for 1st child & 9 fruits to second child is : 10C1*9C9 Number of ways to select 3 fruit for 1st child & 7 fruits to second child is : 10C3*7C7 Number of ways to select 5 fruit for 1st child & 5 fruits to second child is : 10C5*5C5Number of ways to select 7 fruit for 1st child & 3 fruits to second child is : 10C7*3C3Number of ways to select 9 fruit for 1st child & 1 fruits to second child is : 10C9*1C1Total = \(10C1*9C9 + 10C3*7C7 + 10C5*5C5 + 10C7*3C3 + 10C9*1C1\) \(=10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10\) \(=10+120+ 2*9*7*2+ 10*3*4 +10\) \(=10+120+36*7+120+10\) \(=10+120+252+120+10\) \(=260+252=512\) Hence Option C is the answer
_________________
Appreciate any KUDOS given ! MY MBA RESOURCES:



Manager
Joined: 14 Jun 2018
Posts: 223

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
04 Nov 2018, 02:00
(1,9) > 2 ways > 2* 10! / 1!9! = 20 (3,7) > 2 ways > 2* 10!/ 3!7! = 240 (5,5) > 1 way > 10!/5!5! = 252
Total 512



Manager
Joined: 15 Feb 2017
Posts: 244

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
05 Nov 2018, 00:20
Hi guys Is there any other way we can approach this problem. Thanks Sent from my Lenovo K33a42 using GMAT Club Forum mobile app
_________________
IMPOSSIBLE IS JUST AN OPINION



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1199
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
05 Nov 2018, 01:08
sonusaini1Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = 2^10 Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even) Also the probability of both cases are equal = ½ Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ * 2^10 = 2^9 = 512
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Manager
Joined: 04 Jun 2018
Posts: 127

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
05 Nov 2018, 05:00
gmatbusters wrote: sonusaini1Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\) Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even) Also the probability of both cases are equal = ½ Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ *\(2^10\) = \(2^9\) = 512 Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\) Can you explain this? Also, shouldn't the question also mention that the oranges are distinct. It could easily be inferred as similar oranges. IN this case, the answer would have been vastly different.



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1199
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: In how many ways 10 Oranges be distributed among 2 children if both mu
[#permalink]
Show Tags
05 Nov 2018, 06:28
Response to query 1: Total no of ways in which the 10 Oranges be given to 2 person First orange can be given to any of the two person, no of ways = 2 Second orange can be given to any of the two person, no of ways = 2 . . . .Tenth orange can be given to any of the two person, no of ways = 2 total no of ways = = 2*2*2*…2 = 2^10 Response to query 2: Unless it is specifically mentioned that the tems are identical, they are taken as distinct.nitesh50 wrote: gmatbusters wrote: sonusaini1Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\) Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even) Also the probability of both cases are equal = ½ Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ *\(2^10\) = \(2^9\) = 512 Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\) Can you explain this? Also, shouldn't the question also mention that the oranges are distinct. It could easily be inferred as similar oranges. IN this case, the answer would have been vastly different.
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS




Re: In how many ways 10 Oranges be distributed among 2 children if both mu &nbs
[#permalink]
05 Nov 2018, 06:28






