In how many ways can the letters of wordINTELLIGENTbe arranged such that all the Consonants always appear together? Choices
A) 9!	B) 5!*4!	C) 5!*5!	D) 5!*7!	E) 6!*4!
Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (11 letters, 4 vowels I, E, I, E and 7 consonant N, T, L, L, G, N, T)   For all consonants together, consider them as 1 group {N, T, L, L, G, N, T} I E I E --&gt; this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways   Thus total arrangements with all consonants together = 5!*7! --&gt; 5!*7! is the correct answer.
<result>D</result>
In how many ways can the letters of wordINTELLIGENTbe arranged such that all the Consonants always appear together?