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# ID codes issued by XYZ high school have 5 characters. First 2 characte

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Manager
Joined: 20 Mar 2015
Posts: 62

Kudos [?]: 34 [0], given: 9

ID codes issued by XYZ high school have 5 characters. First 2 characte [#permalink]

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12 Jul 2016, 23:54
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ID codes issued by XYZ high school have 5 characters. First 2 characters of the ID codes are vowels and next 3 characters are digits. If ID code of no two students is same, then what is the maximum number of students in XYZ high school?

I thought this was a non repetition question and solved it in the following way:
$$5*4*10*9*8$$
,but the book says that this is a repetition is allowed question. I am confused now?

Book's solutions:

$$5*5*10*10*10$$

Kudos [?]: 34 [0], given: 9

Intern
Joined: 21 Dec 2015
Posts: 12

Kudos [?]: 6 [1], given: 81

ID codes issued by XYZ high school have 5 characters. First 2 characte [#permalink]

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13 Jul 2016, 00:11
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KUDOS
See the first thing you need to realise is they are asking for maximum number of students, which you will get by having maximum choices at hand, And it is maximum when the number are same. So we will consider option for the first one

So first we have 5 vowels and now we want the maximum one it could be same as the previous one. So we have 5 options

Similarly with the numbers also first can be 10 and then second can be 10 and even the third can be 10

Hence it is 5*5*10*10*10

Kudos [?]: 6 [1], given: 81

Manager
Joined: 27 Jan 2013
Posts: 103

Kudos [?]: 79 [0], given: 41

Location: India
GMAT 1: 700 Q49 V35
GPA: 3.7
Re: ID codes issued by XYZ high school have 5 characters. First 2 characte [#permalink]

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13 Jul 2016, 03:29
ID codes issued by XYZ high school have 5 characters. First 2 characters of the ID codes are vowels and next 3 characters are digits. If ID code of no two students is same, then what is the maximum number of students in XYZ high school?

Solution:

Since in the question step it is nowhere mentioned that repetition is not allowed, you must consider repetitions also.

Hence AA000 is as valid as AE987.
Number of vowels =5 {A E I O U}
Number of digits = 10 { 0 1 2 3 4 5 6 7 8 9}

Hence total number of solutions = 5*5*10*10*10.

Please give kudos if this helps!

Kudos [?]: 79 [0], given: 41

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Re: ID codes issued by XYZ high school have 5 characters. First 2 characte [#permalink]

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21 Dec 2017, 06:06
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Re: ID codes issued by XYZ high school have 5 characters. First 2 characte   [#permalink] 21 Dec 2017, 06:06
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