Distinguish b/w a permutation problem and a combination problem.

Great Explanation. Thanks Rick and chetan. I think i should practise more similar questions

Hi
For the 1st question
is it (5p3) + 5!
..??????????

hi dpo28,
the question is...
1. How many different license plates can be made by using either 3 digits or 3 letters assuming that you can use only odd digits and vowels? Repetition is not allowed.

what is the requirement? firstly it will have either odd digits or vowels.. lets take one by one as both are independent...
1) odd digits... 5.. choose 3 out of them but order is imp.. 5P3=5C3*3!...
2) vowels.. 5.. choose three but again order important... 5P3=5C3*3!..
total ways =5C3*3!+5C3*3!=5C3*3!*2=5!..answer

Hi dpo28,

Based on the description in the first example, you can use EITHER 3 numbers (1,3,5,7,9) with NO repeats OR you can use 3 vowels (A,E,I,O,U) with NO repeats.

With a license plate, there is an ORDER to the characters (and the order DOES matter), so we have a permutation.

With just numbers, and 3 "spots" we would have....
5 options for the first 'spot'; once we place a number, we then have....
4 options for the second 'spot'; once we place a number, we then have...
3 options for the third 'spot;
(5)(4)(3) = 60 different licenses with numbers

With just vowels, we have the exact same mathematical situation: 5 vowels and 3 "spots":

5 options for the first 'spot'; once we place a vowel, we then have....
4 options for the second 'spot'; once we place a vowel, we then have...
3 options for the third 'spot;
(5)(4)(3) = 60 different licenses with vowels

60+60 = 120 total licenses under these restrictions.

GMAT assassins aren't born, they're made,
Rich

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