How many words are formed from the word ERUPTION, which

Solution

There are total 8 letters in the given word out of which 4 are consonants (R, P, T, N) and 4 are vowels (E, U, I, O) we have to form a word of 8 letters which have first and last letter consonants. In the beginning and in the last we put 2 consonants out of 3 by ⁴P2 = 12 methods. Now, in between first and last letters 6 letters may be put in ⁶P6 = 6! Therefore, number of words comprises consonant in first and in last will be = = 6! × 12 = 720 × 12 = 8640