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# A license plate has 3 ltrs & 3 digit in tht order. A witness

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Intern
Joined: 19 Mar 2010
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A license plate has 3 ltrs & 3 digit in tht order. A witness [#permalink]

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30 Apr 2010, 13:48
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A license plate has 3 ltrs & 3 digit in tht order. A witness to a hit & run accident saw the first 2 ltrs. & the last digit. If the letter & the digit can be repeated, how many number license plates must be checked by the police to find the culprit?

Also, pls. let me know how many problems involving statistics, probabilities, permutation & combination are in GMAT? If you have any question bank for this or others, pls. do forward.

thanks,
sheetal
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thanks,
SS

Last edited by sheetalsanjana on 30 Apr 2010, 14:10, edited 1 time in total.
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Kudos [?]: 70816 [1] , given: 9857

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30 Apr 2010, 14:04
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Expert's post
sheetalsanjana wrote:
Pls help me with this problem:-

A license plate has 3 ltrs & 3 digit in tht order. A witness to a hit & run accident saw the first 2 ltrs. & the last digit. If the letter & the digit can be repeated, how many number license plates must be checked by the police to find the culprit?

Also, pls. let me know how many problems involving statistics, probabilities, permutation & combination are involved in GMAT? If you have any question bank for this, pls. do forward.

thanks,
sheetal

26 choices for the third letter;
10 choices for the first digit;
10 choices for the second digit.

26*10*10=2600.

P.S. I think at max 1-2 questions from each area (statistics, probabilities, permutation & combination).
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30 Apr 2010, 14:07
but why 10 choice for 1st & 10 choice for 2nd?
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thanks,
SS

Math Expert
Joined: 02 Sep 2009
Posts: 33061
Followers: 5773

Kudos [?]: 70816 [0], given: 9857

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30 Apr 2010, 14:26
Expert's post
sheetalsanjana wrote:
but why 10 choice for 1st & 10 choice for 2nd?

Witness saw first two letters and last digit: LLX-YZD, LL and D is known, X, Y and Z are not.

X can be ANY letter from 26;
Y can be any digit from 10 (0,1,2,..9);
As digits on license can be repeated Z can also be any digit from 10.

Hence 26*10*10=2600.

Hope it's clear.
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30 Apr 2010, 23:02
Another way to think about it, but it gets the same answer:

Think of the 2 digits as any single two digit number. This would be 0-99, or 100 different possibilities.

You know for the missing letter there are 26 possibilities. Each one can be match with any of the 100 two digit numbers, so the answer is 26*100 or 2600.

I realize this may take a bit more time for some people, but I am still mixing up my combs/perms/probs formulas, so sometimes I benefit from working it out this way. Still studying!
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Kudos [?]: 1 [0], given: 11

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01 May 2010, 09:37
thanks you guys...got it
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thanks,
SS

Re: combination problem   [#permalink] 01 May 2010, 09:37
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