Question

find all the arrangements of the word " include" if all constants together ​

Answer 1

Answer:

There are 12 letters in the word interference of which 5 are vowels (4 e's and 1 i) and 7 consonants (2 n's, 2 r's and 1 each of t,f & c) and these 12 letters can be arranged in 12!4!2!2! ways. Now, bunch up the 7 consonants to consider as 1 letter. Then the number of letters in the word interference becomes 6 which can be arranged in 6!4!=30 ways. And these 7 consonants can be arranged among themselves in 7!2!2!=2520 ways. Hence, total number of arrangements in which consonants will never be together is 12!4!2!2!−30∗2520.