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From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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Updated on: 23 Nov 2013, 06:18
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From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning. OA:
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Originally posted by Itzrevs on 28 Dec 2005, 19:45.
Last edited by Bunuel on 23 Nov 2013, 06:18, edited 1 time in total.
Added the OA.



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Re: PS  Probability Consonants & Vowels [#permalink]
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28 Dec 2005, 22:30
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Itzrevs wrote: From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.
Please explain your answer!!!!
Number of ways to choose 4 cons out of 7*Number of ways to choose 3 vowels out of 5>4C7*3C5=(7*6*5*4/1*2*3*4)*(5*4*3/1*2*3)=350



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Re: PS  Probability Consonants & Vowels [#permalink]
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29 Dec 2005, 01:18
Itzrevs wrote: From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.
Please explain your answer!!!!
Since the order of the letters are important we get
7P4*5P3 = 4200



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sorry guys both of you didn't get the OA..
Lets give it another try
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4 consonants can be chosen in 7*6*5*4 ways
3 vowels can be chosen in 5*4*3 ways
Total no. of alternatives =7*6*5*4*5*4*3=50,400



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Re: PS  Probability Consonants & Vowels [#permalink]
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29 Dec 2005, 10:54
krisrini wrote: Itzrevs wrote: From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.
Please explain your answer!!!! Since the order of the letters are important we get 7P4*5P3 = 4200
u have put the right formula but calculated it incorrectly. ur answer shud also be 50400....
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only if i could choose....



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Yurik79, I didn't the same way as you did. But thats not the answer.
I shall wait for few more people to jump in and post their answers & explanations..
Will post the OA soon.
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Re: PS  Probability Consonants & Vowels [#permalink]
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29 Dec 2005, 22:22
crazyfin wrote: krisrini wrote: Itzrevs wrote: From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.
Please explain your answer!!!! Since the order of the letters are important we get 7P4*5P3 = 4200 u have put the right formula but calculated it incorrectly. ur answer shud also be 50400....
Thanks crazyfin. The compuatation should have worked to 50400, I am not sure how I made this mistake, thanks much for pointing out.



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Guys, The OA is 1,764,000
OE :
The 4 different consonants can be selected in 7C4 ways
The different vowels can be selected in 5C3 ways
The resulting 7 different letters ( 4 consonants & 3 vowels) can be arranged themselves in 7P7 = 7! ways..
So the answer is 7C4 * 5C3 * 7! = 35 *10 * 5040 = 1764000
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Itzrevs wrote: Guys, The OA is 1,764,000
OE :
The 4 different consonants can be selected in 7C4 ways The different vowels can be selected in 5C3 ways The resulting 7 different letters ( 4 consonants & 3 vowels) can be arranged themselves in 7P7 = 7! ways..
So the answer is 7C4 * 5C3 * 7! = 35 *10 * 5040 = 1764000
It seemed so simple at first look)))Good one!10x



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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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23 Nov 2013, 06:12
Itzrevs wrote: From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning. Because each word has to consist of different consonants or vowels, the correct answer is (7*6*5*4)*(5*4*3) and not 7^4*5^3. I used bars to distinguish the numbers representing consonants and vowels to make it more clear.



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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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23 Nov 2013, 06:22
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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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25 Nov 2013, 23:13
I do not think you will see like this question in the test, unless the answer choices contain 350 * 7!. but this is a good question to practise both concept  combination and permutation in one question.
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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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01 May 2014, 09:05
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Hi, I still don't get whats wrong with 7P4*5P3?



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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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01 May 2014, 09:53
shashankprasad wrote: Hi, I still don't get whats wrong with 7P4*5P3? That's because we are arranging all 7 letters together. For example, consider simpler case: how many 4letter words you can make from 2 consonants {b, c} and two vowels {a, e}. If you arrange them first ({b, c} and {c, b} for consonants and {a, e} and {e, a} for vowels) you'll get 2*2=4 words, which would be wrong. The correct answer is 4!=24.
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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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01 May 2014, 22:37
Hello there
Are there ways to come up with subtypes of this particular question?
For example,
A case with 3 distinct vowels & 4 distinct consonants. A case where the ORDER of the letters DOES NOT matter (OR) a case where ORDER matters. etc.
OR is there a particular link where such questions are discussed?
Thanks in advance.



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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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02 May 2014, 02:21



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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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02 May 2014, 09:51
Hi Bunuel What is wrong with my approach. Can you please correct me : Imagine 7 boxes now let's say we are filling first 4 boxes with consonants .First box can be filled with 7 ways.Second with 6 and so on. Similarly for 3 vowel boxes : first box can be formed with 5 ways , second with 4 ways and third with 3 ways : So total number of ways =7*6*5*4*5*4*3 And now these letters can be arranged in 7! ways to have different combination. I know I am wrong. Can you please correct me. Thanks in Advance.
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Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]
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02 May 2014, 10:13
282552 wrote: Hi Bunuel What is wrong with my approach. Can you please correct me : Imagine 7 boxes now let's say we are filling first 4 boxes with consonants .First box can be filled with 7 ways.Second with 6 and so on. Similarly for 3 vowel boxes : first box can be formed with 5 ways , second with 4 ways and third with 3 ways :
So total number of ways =7*6*5*4*5*4*3 And now these letters can be arranged in 7! ways to have different combination. I know I am wrong. Can you please correct me.
Thanks in Advance. Short answer would be that 7*6*5*4 as well as 5*4*3 will contain repetitions. The number of way to choose 4 letters out of 7 is NOT 7*6*5*4 it's \(C^4_7=\frac{7!}{4!3!}=35\) and the number of way to choose 3 letters out of 5 is NOT 5*4*3 it's \(C^3_5=\frac{5!}{3!2!}=10\).
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