A five digit number is to be formed using each of the digits : GMAT Problem Solving (PS)
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# A five digit number is to be formed using each of the digits

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A five digit number is to be formed using each of the digits [#permalink]

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05 Sep 2013, 21:29
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A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120
[Reveal] Spoiler: OA
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Re: A five digit number is to be formed using each of the digits [#permalink]

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05 Sep 2013, 21:46
6
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No. of ways the 5 digit number can be formed = 5! = 120

Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48

No. of ways 1 & 2 wont be together = 120 - 48
=72
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Re: A five digit number is to be formed using each of the digits [#permalink]

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05 Sep 2013, 23:06
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MacFauz wrote:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120

No. of ways the 5 digit number can be formed = 5! = 120

Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48

No. of ways 1 & 2 wont be together = 120 - 48
=72

Great solution. +1.

Just to elaborate the case when 1 and 2 are together:

Glue 1 and 2 together and consider them as one unit: {12}.

Now, 4 units {12}, {3}, {4}, and {5} can be arranged in 4! ways and 1 and 2 within their unit can be arranged in 2 ways ({12} or {21}), thus total = 4!*2.
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Re: A five digit number is to be formed using each of the digits [#permalink]

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06 Sep 2013, 03:55
Awesome solutions MacFauz and Bunuel, +1 kudos for both. Thanks a lot
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Re: A five digit number is to be formed using each of the digits [#permalink]

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06 Sep 2013, 03:59
3
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Great learning on this one!! thank you very much!
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Re: A five digit number is to be formed using each of the digits [#permalink]

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06 Sep 2013, 04:07
manuelpalomares wrote:
Great learning on this one!! thank you very much!

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Re: A five digit number is to be formed using each of the digits [#permalink]

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06 Sep 2013, 06:19
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Expert's post
arakban99 wrote:
manuelpalomares wrote:
Great learning on this one!! thank you very much!

No KUDOS?

Good questions deserves kudos as much as a good solution. +1.
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Re: A five digit number is to be formed using each of the digits [#permalink]

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06 Sep 2013, 06:32
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Bunuel wrote:
arakban99 wrote:
manuelpalomares wrote:
Great learning on this one!! thank you very much!

No KUDOS?

Good questions deserves kudos as much as as good solution. +1.

Haha... I second that....
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Re: A five digit number is to be formed using each of the digits [#permalink]

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07 Sep 2013, 05:19
C

Just subtract from the total number of cases.

total number of combinations=5*4*3*2*1=120
When two numbers are together, we will have pack the two numbers together, therefore combinations=4!*2(numbers can be arranged themselves)

The cases where they are not together=total-cases when they are together

120-48=72
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Re: A five digit number is to be formed using each of the digits [#permalink]

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10 Apr 2015, 13:18
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Re: A five digit number is to be formed using each of the digits [#permalink]

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30 May 2016, 20:09
Hello from the GMAT Club BumpBot!

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Re: A five digit number is to be formed using each of the digits [#permalink]

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30 May 2016, 20:33
arakban99 wrote:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120

Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)

5 numbers can be arranged in 5 places in 5! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.

Reqd. Answer = 5! - 4!2! = 120 - (24*2) = 72

Re: A five digit number is to be formed using each of the digits   [#permalink] 30 May 2016, 20:33
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