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# HOw many arrangements of the digits 1,2,3,4,5 are there such

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HOw many arrangements of the digits 1,2,3,4,5 are there such [#permalink]  18 Sep 2005, 14:27
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HOw many arrangements of the digits 1,2,3,4,5 are there such that 2 and 4 are not adjacent?
A)112
B)96
C)72
D)24
E)6
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-Vikram

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[#permalink]  18 Sep 2005, 15:39
I think I got it right but I've got a 50% hit rate on these problems...

Ways to order 5 numbers = 5*4*3*2*1= 120

There are eight ways that 2 and 4 can be adjacent and 3! ways to order the other numbers in each.

8*3*2=48

120-48=72
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[#permalink]  18 Sep 2005, 20:06
i get 72 too..

here is how i did it:

there is a total of 120 (5!) arrangements of the digits 1,2,3,4,5 (with 2 and 4 as adjacent numbers)

now lets take 2 and 4 as a single number (with 2 at the front of 4), then we get 24 (4!) arrangements. and 48 arrangements in total (first with 2 at the front and then with 4 at the front)

so there are 120-48=72 arrangements where 2 and 4 are not adjacent
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[#permalink]  20 Sep 2005, 11:34
there are few things the question misses out

Can a number be repeated?
How many digit numbers are we talking about?

if we assume all 5 digit numbers with no repitition then

120 - (24*2) = 72

if we assume repitition then

5^5 - (2*4^4) = 2613, which is not in the answer so 72
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[#permalink]  20 Sep 2005, 14:42
C it is.....

I would go for the same explanation as Popee

= 5!-(2)(4)(3!)=120-48=72
[#permalink] 20 Sep 2005, 14:42
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# HOw many arrangements of the digits 1,2,3,4,5 are there such

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