Question

Find the number of arrangements of the letters in the word SOLAPUR so that consonants and vowels are placed alternately.

Answer 1

There are 4 consonants S, L, P, R, and 3 vowels A, O, U in the word SOLAPUR. Consonants and vowels are to be alternated.

∴ Vowels must occur in even places and consonants in odd places.

∴ 3 vowels can be arranged at 3 even places in ³P₃ = 3! = 6 ways.

Also, 4 consonants can be arranged at 4 odd places in ⁴P₄ = 4! = 24 ways.

Required number of arrangements = 6 × 24 = 144