Permutation & Combination

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

shivanigs: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri Apr 27, 2012 5:10 am; Followed by:2 members

Permutation & Combination

by shivanigs » Fri Jul 20, 2012 2:53 am

Hi,

Request your help to understand the logic behind this question.Thanks..

In how many ways can 3 people out of 14 people be given 3 prizes (gold,silver and bronze) so that Jack is awarded? Jack is one of the 14 people.

I don't have the OA for this one.

Quote

Source: Beat The GMAT — Problem Solving | Fri Jul 20, 2012 2:53 am

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pm; Thanked: 339 times; Followed by:49 members; GMAT Score:770

by eagleeye » Fri Jul 20, 2012 3:25 am

shivanigs wrote:Hi,

Request your help to understand the logic behind this question.Thanks..

In how many ways can 3 people out of 14 people be given 3 prizes (gold,silver and bronze) so that Jack is awarded? Jack is one of the 14 people.

I don't have the OA for this one.

Hi shivanigs:

Since Jack must be awarded, he is always present among the prize winners. Then we need to select the other remaining 2 people from the 13 left for the other two prizes. No. of ways of selecting 2 people out of 13 = 13C2 = 13*6.
We are not done yet. We have 3 people but we can arrange the prizes between them in a number of ways.
No. of ways of awarding 3 people 3 prizes, when each gets only one = (choices for 1st prize)*(remaining choices for 2nd prize)*(last choice remaing after awarding 2 prizes) = 3*2*1=3!.

So total number of ways required= 13C2*3! = 13*6*6= 13*36= 468.

Quote

karthik4vj: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Jul 20, 2012 7:43 am

by karthik4vj » Fri Jul 20, 2012 11:33 pm

I used combination of both probablity and permutation. Not sure if it is right approach. Here we go ..

Step 1:
Number of ways to chose 3 winners out of 14 people = 14! / 11! = 2184

Step 2:
Probability that Jack is one among the winners = 3/14

Step 3:
Product of the above two steps should give u the answer = 2184 * (3/14) = 468