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

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Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 13 Mar 2015, 05:38
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I find its really tough to do P&C problems. How do i find whether it is a permutation or a combination problem? Should i look for any key words in the question stem?

I have three questions. Is there any general rule to find which one is permutation and which one is combination?

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.

2. How many 3 letter words can be formed from the alphabets A-F such that the word contains 1 vowel and 2 consonants? Repetition is not allowed and the words need not make sense.

3. How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets is not allowed?
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Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 13 Mar 2015, 09:21
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I find its really tough to do P&C problems. How do i find whether it is a permutation or a combination problem? Should i look for any key words in the question stem?

hi,
at times the wording of the question does tell you what to use..
1) if the Q asks you to find combinations, selection, order not important, etc you got to use combinations formula...a!/b!(a-b)!...
2) if the Q asks you to find permutations, arrangements, order important, etc you got to use permutations formula...a!/(a-b)!..


I have three questions. Is there any general rule to find which one is permutation and which one is combination?

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.
order is important as 315 will give different plate from 153... so permutation

2. How many 3 letter words can be formed from the alphabets A-F such that the word contains 1 vowel and 2 consonants? Repetition is not allowed and the words need not make sense.
same as 1 order is important .. first it will be ways of choosing these vowel and consonants so combination but then arranging them will involve in permutation that is these ways will be multiplied by 3!

3. How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets is not allowed?
for this first you find the ways to choose the two alphabets and then 4! to arrange thes..
G and L already chosen.. so 2 out of 5=5C2=10...
these 4 can be arranged in 4! ways
ans=10*4!...

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Re: Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 13 Mar 2015, 11:53
Hi TARGET730,

Permutations and Combinations are relatively rare categories on Test Day. You'll probably see at least 1 of each, but even if you're performing really well in the Quant section you like won't see more than 2-3 of each.

The 'big' difference between these two question types is about 'order' - when reading through the question, you have to ask yourself IF order 'matters'. If it does, then it's a Permutation question; if it does NOT, then it's a Combination question. Thankfully, the questions themselves often offer clues (e.g. the word "arrangement" means Permutation, the word "combinations" means Combination).

All 3 of the examples that you provided are clearly about putting elements in "order": forming license plates or making words is an 'order-specific event.'

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New post 15 Mar 2015, 05:49
Great Explanation. Thanks Rick and chetan. I think i should practise more similar questions
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Re: Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 15 Mar 2015, 06:16
Hi
For the 1st question
is it (5p3) + 5!
..??????????
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Re: Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 15 Mar 2015, 06:27
@dpo28 wrote:
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
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Re: Distinguish b/w a permutation problem and a combination problem.  [#permalink]

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New post 15 Mar 2015, 18:32
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.

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Re: Distinguish b/w a permutation problem and a combination problem.   [#permalink] 29 Jan 2018, 00:01
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