Question

9.How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time,
such that the four vowels do not come together?
A) 216 B) 45360
C) 1260 D) 43200​

Answer 1

Answer:

43200

option D is correct

Step-by-step explanation:

First find total possible arrangements of

COMMITTEE

total 9 letters

M , T & E are repeated

= 9!/(2! 2! 2!)

= 45360

Now find all arrangement where 4 Vowels Come together

Taking 4 vowels as one group  & 5 letters

making it total 6

so arrangements

= 6!* 4! / (2! 2! 2!)

= 2160

arrangements such that the four vowels do not come together

= 45360 - 2160

= 43200

Answer 2

Answer:

Step-by-step explanation:

First find total possible arrangements of

COMMITTEE

total 9 letters

M , T & E are repeated

= 9!/(2! 2! 2!)

= 45360

Now find all arrangement where 4 Vowels Come together

Taking 4 vowels as one group & 5 letters

making it total 6

so arrangements

= 6!* 4! / (2! 2! 2!)

= 2160

arrangements such that the four vowels do not come together

= 45360 - 2160

= 43200