Question

In how many ways the word CATHOLICS are arranged such that all that all the vowels should be in odd positions.

Answer 1

Answer:

21600

Step-by-step explanation:

CATHOLICS

Vowels - A  O  I  

Consonant - C , T , H , L S C

Odd positions  1 , 3 , 5 , 7 , 9  = 5 Posistions

all the vowels

3 Vowels can be positioned

in ⁵P₃ = 5!/(5-3)!  = 5!/2!  = 60

Remaining positions

9 - 3 = 6

6 Positions can be filled

in 6!/ 2!    ways  as  C is repeated

= 360

Total = 360 * 60

= 21600