Question

calculate the number of arrangement of letters of the word include if no two consonants are together​

Answer 1

Answer:

the word INCLUDE has four constants N,C,L,D and three vowels I,U,E. No two letters are repeating.

in order to keep the constants apart, the arrangement should be like given below

CVCVCVC (C for constant, V for vowel)

now the three vowels can be arranged in 3! ways, the four constants can be arranged in 4! ways

hence total number of arrangement is 3!*4!

= 6*24

= 144