Question

In how many ways can the letters of the word “AFLATOON” be arranged if the consonants and vowels must occupy alternate places? 

(a) 176 

(b) 144 

(c) 136 

(d) 288

Answer 1

(d) 288

There are 8 letters in the word AFLATOON out of which 4 are vowels, i.e., A, A, O, O and 4 are consonants, i.e., F, L, T, N. 

There are 2 ways in which the 4 consonants and 4 vowels occupy alternate places: 

VC  VC  VC  VC or CV  CV  CV  CV 

where V–vowel, C–consonant. 

The four vowels can be arranged in 4 places in \(\frac{4!}{2!2!}\) ways = 6 ways 

The four consonants can be arranged in their 4 places in 4! ways = 24 ways. 

Also, there are 2 cases, so, 

∴Required number of permutations = 6 × 24 × 2 = 288.