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# How many 5 letters words can be formed using BEGIN?

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Manager
Joined: 10 Dec 2011
Posts: 102
Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
How many 5 letters words can be formed using BEGIN? [#permalink]

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18 Sep 2017, 12:21
2
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:35) correct 22% (01:16) wrong based on 83 sessions

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How many 5 letters words can be formed using BEGIN?

Condition: Vowels must come at the end

A. 10
B. 12
C. 20
D. 24
E. 15

I would like if someone solves this through the nPr method. Bunuel come on man!
Math Expert
Joined: 02 Sep 2009
Posts: 46305
Re: How many 5 letters words can be formed using BEGIN? [#permalink]

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18 Sep 2017, 12:25
1
talismaaniac wrote:
How many 5 letters words can be formed using BEGIN?

Condition: Vowels must come at the end

A. 10
B. 12
C. 20
D. 24
E. 15

I would like if someone solves this through the nPr method. Bunuel come on man!

E - - - I

3 consonants in the middle can be arranged in 3! ways, and E and I can be arranged in 2! ways (E - - - I and I - - - E), so 3!*2! = 12.

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Re: How many 5 letters words can be formed using BEGIN? [#permalink]

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19 Sep 2017, 03:10
talismaaniac wrote:
How many 5 letters words can be formed using BEGIN?

Condition: Vowels must come at the end

A. 10
B. 12
C. 20
D. 24
E. 15

I would like if someone solves this through the nPr method. Bunuel come on man!

Let us arrange the consonants first in the 3 places.
It can be done in 3x2x1=6 ways which is same as 3P3.
vowels can be arranged in 2! = 2 ways
hence answer = 6x2 =12 ways (B)

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Manager
Joined: 17 Aug 2016
Posts: 51
Re: How many 5 letters words can be formed using BEGIN? [#permalink]

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19 Sep 2017, 12:52
1
talismaaniac wrote:
How many 5 letters words can be formed using BEGIN?

Condition: Vowels must come at the end

A. 10
B. 12
C. 20
D. 24
E. 15

I would like if someone solves this through the nPr method. Bunuel come on man!

Here are two methods -

BEGIN has two vowels - E and I, they need to come at the end.

__ __ __ I E
Fix E at the end, and I next to it, then we would be left with 3 alphabets that needs to be arranged at the remaining 3 places, that can be done in 3P3 = 3! = 6 ways.

__ __ __ E I
Similarly if we fix I at the end and E next to it, we can fill the remaining 3 places in 3P3 ways = 6 ways.

Total words that can be formed with vowels at the end would be = 6 * 2 = 12 ways.

Method 2 -

BEGIN -

E and I at the end.(they can be filled at the end in 2 ways)

_1_ x__2_x _3__ x_1_ x __2__ = 12 ways

This is the filling spaces method, which I prefer than using the nPr formula.

Regards,
Squib
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Re: How many 5 letters words can be formed using BEGIN?   [#permalink] 19 Sep 2017, 12:52
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