Question

in how many ways can the letters of the word 'cinema' be arranged so that the order of vowels do not change​

Answer 1

Answer:

Total ways = 120

Step-by-step explanation:

CINEMA

TOTAL = 6

VOWELS = A , E  & I  = 3

CONSONANTS = 3   (C , N , & M)

3 Consonant in 6 positions can be arranged in

⁶P₃ ways

= 6!/3!

= 6 * 5 * 4

= 120

Vowels now can be arranged in one way only

³C₃ = 1

Total ways = 120 * 1 = 120

or 3 Vowels out of 6 position in

⁶C₃ ways  as order is defined

= 6!/(3!3!) = 20

and now 3 Consonants in remaining 3 Positions

= ³P₃  = 3! = 6

Total Ways = 20*6 = 120