How many arrangements are possible with the letters of the

Question

How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

Bunuel · Answer

There are 4 consonants (P, R, F and L) and 3 vowels (O, I and E) in PROFILE. Consider the following: *O*I*E*.

If we place the consonants instead of stars no two consonants will be together. 4 consonants, in places of 4 stars can be arranged in 4! ways and 3 vowels can be arranged in 3! ways, so the total of 4!*3! = 144.

Answer: C.

luffy_ueki · Answer

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In 'PROFILE': P,R,F,L are the consonants, the only way they cannot come together is by arranging the vowels (I,E,O) between them i.e. in the blanks aas can be seen below:
P_R_F_L

Lets arrange it:
1. Arrangement of P,R,F,L = 4! ,and 
2. Arrangement of blanks which has I,E,O = 3!

Totoal =4!*3!

Phuonganhtran · Answer

Here we have 3 vowels (O,I,E) and 4 consonants (P,R,F,L). Since no 2 consonants are to come together, the positions of consonants are * and vowels are _ as following: *_*_*_*.
 We have 4! ways to arrange 4 consonants into 4 positions and 3! ways to arrange 3 vowels into 3 positions.
Consequently there are 4!*3!=144 arrangements.

How many arrangements are possible with the letters of the

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How many arrangements are possible with the letters of the

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