Question

15. 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

hope it is helpful for you

Answer 2

Answer:

First:

To find the no. of ways of arranging letters in the word PLATOON such that no the two O's are together, we can subtract the no. of ways in which two O's are together from the total no. of ways.

Total no. of ways = 7! / 2! = 2520

Because O is repeated 2 times in the word.

Now the two O's are considered as a single objec, so there are 6 letters in the word PLAT[OO]N and thus the no. of arrangements is 6! = 720. The two O's can be permuted only in 2! / 2! = 1 way.

Thus the no. of ways in which the two O's are together

= 6! × (2! / 2!)

= 720

Hence required no. of arrangements

= 2520 - 720

= 1800

Second :

Let me indicate consonants as C and vowels as V. There are 4 spaces required for consonants and 3 for vowels in the word. So we can only arrange the letters as the following.

CVCVCVC

The consonants can be arranged in these 4 spaces in 4! = 24 ways. The vowels can be arranged in these spaces in 3! / 2! = 3 ways, since O is repeated 2 times.

Hence the required no. of arrangements

= 24 × 3

= 72

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