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by Options » Sun Jul 03, 2011 8:23 am
hey guys need a hand here :( cant seem to solve it correctly D:

Calculate the number of arrangements of the letters of the word INCLUDE if
a. all the consonants are together
b. no two consonants are together
c. each arrangement begins with a consonant and ends with a vowel.
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by Frankenstein » Sun Jul 03, 2011 9:05 am
Hi,
include -
Vowels: i,u,e
consonants: n,c,l,d
a) i,u,e,group of (n,cl,d) can be arrnaged in 4! ways
(n,c,l,d) are arranged in 4! ways.
so, total 4!*4! ways
b)_i_u_e_
vowels can be arranged in 3! ways.
consonants in the 4 blanks in 4!ways
So, total 3!*4! ways
c)first letter can be picked from 4 consonants in 4 ways
last letter from 3 vowels in 3 ways
remaining 5 in 5! ways
So, total 4.3.5! ways.
Cheers!

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