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

Step-by-step solution

The word SOLAPUR consists of 7 letters. The vowels are O, A, U (3 vowels). The consonants are S, L, P, R (4 consonants). Since consonants and vowels must be placed alternately and there are 4 consonants and 3 vowels, the arrangement must start and end with a consonant. The only possible pattern is C V C V C V C, where C represents a consonant and V represents a vowel. The 4 consonants can be arranged in the 4 alternate positions in 4! ways. The 3 vowels can be arranged in the 3 remaining alternate positions in 3! w