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

Redeem

Permutation and combination

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 91
Joined: Fri Jan 17, 2014 7:34 am
Thanked: 7 times

Permutation and combination

by parveen110 » Fri Jan 24, 2014 9:37 am
X is the set of all the pairs (p,q) where 1<=p<q<=N. If two distinct members of X have one constituent of the pairs in common, they are called "mates" otherwise they are called "non-mates". For example, If N=4, X={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)} then (1,2) and (1,3) are mates (1,2), (2,3) are also mates, but (1,4),(2,3) are non-mates.

1. Find the number of non-mates that each member of X has for N=7.
a. 10
b. 36
c. 28
d. 21

OA a

2. If two members of X are mates, how many other members of X will be common mates of both these members for N=9?
a. 5
b. 7
c. 11
d. 10

OA b
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

by Patrick_GMATFix » Fri Jan 24, 2014 10:18 am
Just think of the integers as different numbers that get grouped into pairs. Two groups are considered "mates" if the same number belongs to both groups and "non-mates" if the two groups have no overlap.

With that, rephrase the question.

Q1. For any given pair, how many other pairs will have no overlap? (use #s 1 through 7 only)

Suppose the given pair is (1,2). This question simply becomes how many other pairs can we make form the 5 unused numbers? In other words, how many ways are there to pick 2 from 5? This is 5!(2!3!) = 10.

Q2. Given two pairs that share a common number, how many other pairs will have that number? (use #s 1 through 9 only)

Suppose the initial mates are (1,2) and (1,3). there are only six other pairs that will be mates to both original mates: (1,4), (1,5), (1,6), (1,7), (1,8) and (1,9)
  • Ask me about tutoring.
Top
Post new topic Post Reply
• Page 1 of 1