In how many ways can the letters of wordTREATMENTbe arranged such that all the Consonants always appear together?  Pick one: A) 9! B) 4!*6! C) 5!*5! D) 5!*4!*2! E) 6!*4!
Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 3 vowels e, a, e and 6 consonant t, r, t, m, n, t)   For all consonants together, consider them as 1 group {t, r, t, m, n, t} E A E --&gt; this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways   Thus total arrangements with all consonants together = 4!*6! --&gt; 4!*6! is the correct answer.
<result>B</result>
In how many ways can the letters of wordTREATMENTbe arranged such that all the Consonants always appear together?