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# Out of six consonants and three vowels,how many words can be made so

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Manager
Joined: 08 Sep 2010
Posts: 150
Location: India
WE 1: 6 Year, Telecom(GSM)
Out of six consonants and three vowels,how many words can be made so  [#permalink]

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Updated on: 28 Oct 2010, 00:59
11
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:11) correct 46% (01:55) wrong based on 94 sessions

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Out of six consonants and three vowels,how many words can be made so that each word contains two consonants and three vowels.

A. 1800
B. 15
C. 18
D. 1600
E. 24

Originally posted by ankitranjan on 26 Oct 2010, 21:02.
Last edited by ankitranjan on 28 Oct 2010, 00:59, edited 1 time in total.
Intern
Joined: 11 Sep 2010
Posts: 2
Re: Out of six consonants and three vowels,how many words can be made so  [#permalink]

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26 Oct 2010, 23:02
6C2 x 3C3 x 5! = 1800

Manager
Joined: 24 Jun 2017
Posts: 117
Re: Out of six consonants and three vowels,how many words can be made so  [#permalink]

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30 Jul 2017, 12:04
aarthic wrote:
6C2 x 3C3 x 5! = 1800

or
4! * 1 * 5! = 24 * 120 = 2880
Am i missing something? How did you get 1800?
Intern
Joined: 21 Sep 2016
Posts: 29
Re: Out of six consonants and three vowels,how many words can be made so  [#permalink]

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12 Aug 2017, 23:58
cbh wrote:
aarthic wrote:
6C2 x 3C3 x 5! = 1800

or
4! * 1 * 5! = 24 * 120 = 2880
Am i missing something? How did you get 1800?

We're choosing 2 consonants out of a group of 6, so it is irrelevant if we get (B,C) or (C,B). The same applies for the vowels.
After picking the five letters up, and since the new words aren't required to have a meaning, we can mix them up through 5!.
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: Out of six consonants and three vowels,how many words can be made so  [#permalink]

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13 Feb 2019, 20:49
ankitranjan wrote:
Out of six consonants and three vowels,how many words can be made so that each word contains two consonants and three vowels.

A. 1800
B. 15
C. 18
D. 1600
E. 24

Position is not fixed, and they can even take multiple values

With that in mind, number of ways will be

5!/ 3! * 2! * 6*5*3*2*1

1800

A
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Manager
Joined: 23 Aug 2017
Posts: 117
Out of six consonants and three vowels,how many words can be made so  [#permalink]

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14 Feb 2019, 01:17
I was trying to solve it in a different way:
Given: 6 consonants and 3 vowels
To make 5 letter word having 2 conso and 3 vowels.
So imagining we have to fill the 5 slots , we can 1st consider the consonants. Since the order of the consonants also matter we can have 5P2 numbers of slots with 2 consonants. Since we can repeat the consonants, for each of the 2 slots we have 6 choices. Thus the total no of ways of consonants: 5P2*6*6
Now for each of these cases considering 3 vowels in 3 slots and no restriction on repeating them, no of diff ways: 3*3*3...

Out of six consonants and three vowels,how many words can be made so   [#permalink] 14 Feb 2019, 01:17
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