Number of permutations of ‘n’ things, taken ‘r’ at a time, : Ask GMAT Experts
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 08:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Number of permutations of ‘n’ things, taken ‘r’ at a time,

Author Message
Intern
Joined: 29 Mar 2013
Posts: 16
Followers: 1

Kudos [?]: 23 [0], given: 12

Number of permutations of ‘n’ things, taken ‘r’ at a time, [#permalink]

### Show Tags

18 Apr 2013, 14:28
Hi,
Can anyone please give me example for this -

Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is to be always included in each arrangement

= r x P(n-1 r-1)
VP
Joined: 23 Mar 2011
Posts: 1113
Concentration: Healthcare, Strategy
Schools: Duke '16 (M)
Followers: 78

Kudos [?]: 496 [1] , given: 463

Re: Number of permutations of ‘n’ things, taken ‘r’ at a time, [#permalink]

### Show Tags

19 Apr 2013, 02:46
1
KUDOS
you have 6 numbered balls - from 1 to 6. You need to select 3 balls such that ball that is numbered '4' is always selected. Additionally, you need to arrange them in bags A B and C.

In essence you are selecting 2 balls from the remaining 5 balls and subsequently, arranging the 3 balls in bags A B and C.
Cases:
1.) you can place the ball#4 in A , and arrange the remaining 2 balls in B and C - in 5P2 ways OR
2.) you can place the ball#4 in B , and arrange the remaining 2 balls in A and C - in 5P2 ways OR
3.) you can place the ball#4 in C , and arrange the remaining 2 balls in B and A - in 5P2 ways

so the total cases are 3 x 5P2 i.e. r x (n-1)P(r-1)

In short, select 2 balls out of remaining 5 in 5C2 ways and arrange the 3 balls in 3! ways. Hence, 3! x 5C2 = 3 x 5P2 = r x(n-1)P(r-1)
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7121
Location: Pune, India
Followers: 2133

Kudos [?]: 13638 [1] , given: 222

Re: Number of permutations of ‘n’ things, taken ‘r’ at a time, [#permalink]

### Show Tags

19 Apr 2013, 07:57
1
KUDOS
Expert's post
iwantto wrote:
Hi,
Can anyone please give me example for this -

Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is to be always included in each arrangement

= r x P(n-1 r-1)

Think of the formula in this way:

You have n total things, say 10. You need to select r out of those, say 4, such that one of those, say a red ball, is always included.

If you have to select and arrange 4 things out of 10, you use 10p4. Now since the red ball must always be included, we need to select only 3 out of 9 things.

We select and atrrange 3 things out of 9 in 9P3 ways i.e. (n-1)P(r-1). Now the problem leftover is where do you put the red ball? There are 4 places to put the red ball. Before the first thing, before the second thing, before the third thing and after the third thing. Hence, you multiply 9P3 by 4. You get

r * (n-1)P(r-1)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: Number of permutations of ‘n’ things, taken ‘r’ at a time,   [#permalink] 19 Apr 2013, 07:57
Similar topics Replies Last post
Similar
Topics:
Probability, Permutations and Combinations Questions 8 13 Dec 2016, 23:20
7 Permutation Combination conceptual issue. 3 05 Sep 2013, 01:31
1 taken gmat 4 times and always landed around 600.wht to do? 3 19 Dec 2012, 23:51
1 For a certain set of N numbers where N>1 is the average (ari 2 31 Jan 2012, 08:31
1 Taken by a surprise 3 12 Sep 2011, 22:16
Display posts from previous: Sort by