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# How many positive five-digit even integers can be formed

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Manager
Joined: 25 Feb 2008
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How many positive five-digit even integers can be formed [#permalink]  21 Mar 2008, 05:19
How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?
1
10
16
24
120
Optional: time you spend on this question
Manager
Joined: 20 Aug 2007
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Re: five-digit even integer [#permalink]  21 Mar 2008, 05:46
Capthan wrote:
How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?
1
10
16
24
120
Optional: time you spend on this question

To make it even, last digit must be 2 only
for the rest, _ _ _ _ 2
all possible = 4*3*2*1 = 24
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Re: five-digit even integer [#permalink]  21 Mar 2008, 05:52
what would be the answer if repitition was allowed?

4*4*4*4?
Manager
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Re: five-digit even integer [#permalink]  21 Mar 2008, 06:53
fresinha12 wrote:
what would be the answer if repitition was allowed?

4*4*4*4?

I'd say 5*5*5*5 because 2 can be included as well
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Re: five-digit even integer [#permalink]  21 Mar 2008, 07:01
Im not sure I understand. There are 5 different numbers, what would be the repetitions?
SVP
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Re: five-digit even integer [#permalink]  21 Mar 2008, 07:13
Capthan wrote:
How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?
1
10
16
24
120
Optional: time you spend on this question

5 digit integer: a b c d e
e can have only 2 to make the numbers even.
so we can fill only abcd by integers 3, 5, 7, and 9. so they can be filled in 4! (or 24) ways since no repetation is allowed.

if repetation is allowed: abcde = 5x5x5x5x5 = 5^5.
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Manager
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Re: five-digit even integer [#permalink]  21 Mar 2008, 07:41
GMAT TIGER wrote:
Capthan wrote:
How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?
1
10
16
24
120
Optional: time you spend on this question

5 digit integer: a b c d e
e can have only 2 to make the numbers even.
so we can fill only abcd by integers 3, 5, 7, and 9. so they can be filled in 4! (or 24) ways since no repetation is allowed.

if repetation is allowed: abcde = 5x5x5x5x5 = 5^5.

if no repetition is allowed, given same other conditions, shouldn't it be 5^4 because the last digit must still be 2 only
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Re: five-digit even integer [#permalink]  21 Mar 2008, 08:32
so the answer to this question is 24.

_ _ _ _ _

in the last spot,we must have 2 to make the number even. in the other four spots, we can put any of the 4 remaining #s, but since repitition is not allowed, we have 4 x 3 x 2 x 1 x 1 = 24
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Re: five-digit even integer [#permalink]  21 Mar 2008, 20:48
prov wrote:
GMAT TIGER wrote:
Capthan wrote:
How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?1101624120Please explain your answer. Optional: time you spend on this question

5 digit integer: a b c d ee can have only 2 to make the numbers even.so we can fill only abcd by integers 3, 5, 7, and 9. so they can be filled in 4! (or 24) ways since no repetation is allowed.if repetation is allowed: abcde = 5x5x5x5x5 = 5^5.
if no repetition is allowed, given same other conditions, shouldn't it be 5^4 because the last digit must still be 2 only

if repetition is allowed, given same other conditions, = 5^4 because the last digit must be 2 only.
if repetation is allowed (I mean without any condition): abcde = 5x5x5x5x5 = 5^5.
_________________
Re: five-digit even integer   [#permalink] 21 Mar 2008, 20:48
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