GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Apr 2020, 07:19

### 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
Your Progress

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

# How many different numbers can we have by changing the position of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Jan 2015
Posts: 25
How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

24 Feb 2015, 01:56
2
00:00

Difficulty:

15% (low)

Question Stats:

71% (00:54) correct 29% (01:15) wrong based on 100 sessions

### HideShow timer Statistics

How many different numbers can we have by changing the position of the digits of the number 718844?

a) 15
b) 90
c) 180
d) 360
e) 720
Math Expert
Joined: 02 Sep 2009
Posts: 62542
Re: How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

24 Feb 2015, 03:35
2
1
Awli wrote:
How many different numbers can we have by changing the position of the digits of the number 718844?

a) 15
b) 90
c) 180
d) 360
e) 720

THEORY

Permutations of $$n$$ things of which $$P_1$$ are alike of one kind, $$P_2$$ are alike of second kind, $$P_3$$ are alike of third kind ... $$P_r$$ are alike of $$r_{th}$$ kind such that: $$P_1+P_2+P_3+..+P_r=n$$ is:
$$\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}$$

For example number of permutation of the letters of the word "gmatclub" is $$8!$$ as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is $$\frac{6!}{2!2!}$$, as there are 6 letters out of which "g" and "o" are represented twice.

According to the above, the number of arrangements of 6-digit number 718844, where 8's and 4's are repeated twice is 6!/(2!2!) = 180.

Answer: C.

Hope it's clear.
_________________
Intern
Joined: 08 Jan 2015
Posts: 25
Re: How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

24 Feb 2015, 03:38
Bunuel wrote:
Awli wrote:
How many different numbers can we have by changing the position of the digits of the number 718844?

a) 15
b) 90
c) 180
d) 360
e) 720

THEORY

Permutations of $$n$$ things of which $$P_1$$ are alike of one kind, $$P_2$$ are alike of second kind, $$P_3$$ are alike of third kind ... $$P_r$$ are alike of $$r_{th}$$ kind such that: $$P_1+P_2+P_3+..+P_r=n$$ is:
$$\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}$$

For example number of permutation of the letters of the word "gmatclub" is $$8!$$ as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is $$\frac{6!}{2!2!}$$, as there are 6 letters out of which "g" and "o" are represented twice.

According to the above, the number of arrangements of 6-digit number 718844, where 8's and 4's are repeated twice is 6!/(2!2!) = 180.

Answer: C.

Hope it's clear.

Very clear. Thank you very much Bunuel!
Intern
Joined: 08 Jan 2015
Posts: 25
Re: How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

24 Feb 2015, 10:44
chetan2u wrote:
6!/2!2!=180
ans C

Thank you very much!
SVP
Joined: 06 Nov 2014
Posts: 1865
Re: How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

28 Feb 2015, 07:38
Awli wrote:
How many different numbers can we have by changing the position of the digits of the number 718844?

a) 15
b) 90
c) 180
d) 360
e) 720

Permutation in a group where there are repeated elements = n!/(p! * p2! *...*pn!); where p1, p2, .., pn are the number of times the element is repeated.
So, here required numbers = 6!/(2! * 2!) since we have 6 digits and 8 and 4 are each repeated twice.
= 180
Hence option C

--
Optimus Prep's GMAT On Demand course for only \$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Non-Human User
Joined: 09 Sep 2013
Posts: 14469
Re: How many different numbers can we have by changing the position of the  [#permalink]

### Show Tags

02 Sep 2016, 23:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: How many different numbers can we have by changing the position of the   [#permalink] 02 Sep 2016, 23:37
Display posts from previous: Sort by

# How many different numbers can we have by changing the position of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne