Question

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

Answer 1

In the word 'SOLAPUR', the number of letters is n = 7.

Vowels are O, A, U, and consonants are S, L, P, R

Since consonants and vowels are placed alternately, the four consonants must occur at 4 odd places and three vowels must occur at 3 even places.

Now, 4 consonants can be arranged in ⁴P₄ ways and 3 vowels can be arranged in ³P₃ ways.

Hence, the number of arrangements in which consonants and vowels are placed alternately

= ⁴P₄ × ³P₃

= 4!3!

= 4 × 3 × 2 × 1 × 3 × 2 × 1

= 144