Question

Find the number of different ways of arranging letters in the word PLATOON if.
(a) the two O’s are never together. (b) consonants and vowels occupy alternate positions.​

Answer 1

Answer:  a) 1800       b) 72

Step-by-step explanation:

a) The two O's are never together

Total No. of ways  =  7! 2! = 2520.....[Because O repeated two times]

Now, Consider two O's as single

No.  of ways = 6! = 720

The two O's can be permuted only 2!/ 2! = 1 way

The No. of ways in which two O's are together = 6!  x 1 = 720

Hence No. of arrangements = 2520 - 720 = 1800

b) Let the Consonants C and vowels V. 4 Spaces are required for consonant and 3 for vowel in the word.

CVCVCVC

Consonant arrangement  = 4! = 24 ways

Vowel arrangement  = 3! / 2! = 3 ways

The No. of arrangement required = 24 x 3 = 72