There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
A) 100
B) 90
C) 50
D) 45
E) 25
The answer should be D. Could anyone take me through this problem please?
Day Care Problem
This topic has expert replies
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
When we want to know the number of possible subgroups that we can make out of a big group, we use the combinations formula, which is:adi wrote:There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
A) 100
B) 90
C) 50
D) 45
E) 25
The answer should be D. Could anyone take me through this problem please?
nCk = n!/k!(n-k)!
n = total number of objects
k = number we want in each group
Here, we have 10 total objects and we're making groups of 2, so n=10 and k=2.
10C2 = 10!/2!(10-2)! = 10!/2!8! = 10*9*8!/2*8! = 10*9/2 = 90/2 = 45
If you're hoping to do well on the GMAT, the combinations formula is one that you need to know (and know well). The question you posted is on the low-end of difficulty for combinations questions (since it only requires knowing the basic formula and plugging in numbers from a simple scenario).
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Tue Jan 22, 2013 8:48 pm
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
Exactly!thinktank08 wrote:10C2 = (10*9)/2*1 = 45
Keep it simple
If anyone is interested, we have a free video on calculating combinations (like 10C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
Cheers,
Brent
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
let 10 students are
1,2---10
pairs of 1 =9
pairs of 2 = 8 bcz (1,2) and (2,1) are same
paire of 3 = 7
-
-
pair of 9 = 1= (9,10)
ans = 9+8+7+6+5+4+3+2+1 = 45
1,2---10
pairs of 1 =9
pairs of 2 = 8 bcz (1,2) and (2,1) are same
paire of 3 = 7
-
-
pair of 9 = 1= (9,10)
ans = 9+8+7+6+5+4+3+2+1 = 45
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7294
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:adi wrote: ↑Sat Mar 08, 2008 2:36 pmThere are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
A) 100
B) 90
C) 50
D) 45
E) 25
The answer should be D. Could anyone take me through this problem please?
Since 2 children are selected from 10 and the order of selection doesn’t matter, there are 10C2 = (10 x 9)/2 = 45 different pairs.
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews