How many 5 letters words can be formed using BEGIN?

Question

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!

Bunuel · Accepted Answer

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.

Answer: B.

souvonik2k · Answer

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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Squib17 · Answer

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

MHIKER · Answer

BEGIN
The total letters are 5 and words consisting 5 letters will be formed with Vowels at the end. 
Number of Vowels are 2; E AND I
So, we have 3 letters; BGN to fill first three position and EI to fill the last two position.

Thus, we will have 
3 letters for the first position (CONSONENT)
2 letters for the second position (CONSONENT), and 
1 letter for the third position (CONSONENT)

SIMILARLY, 
2 letters for the fourth position (VOWEL)
1 letter for the fifth position (VOWEL)

Hence, we have: 
3x2x1x2x1 = 12, or
3!2!= 12.

Ans. B

Fdambro294 · Answer

I guess I interpreted the Question Wrong, but still came up with the Correct Answer:

___ : ____ : ____ : Vowel : Vowel

3 Consonants can be Arranged in the 1st 3 Spot in 3! Ways

AND

We can Arrange the 2 Vowels in the Last 2 Spots in 2! Ways

3! * 2! = 12 Ways
-B-

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How many 5 letters words can be formed using BEGIN?

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How many 5 letters words can be formed using BEGIN?

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