In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?A360B480C720D5040ENone of these
Question
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
A) 360
B) 480
C) 720
D) 5040
E) None of these
Solution
To solve this problem, we first consider the vowels EA and I as a single letter. So, we have the letters L, N, D, G, and 'vowel group' to arrange, which gives us 5! (5 factorial) ways to arrange these letters.
5! = 54321 = 120
Next, within the 'vowel group' of EA and I, we have 3! (3 factorial) ways to arrange these letters.
3! = 321 = 6
So, the total number of ways to arrange the letters in 'LEADING' such that the vowels always come together is 120*6 = 720.
Therefore, the answer is C720.
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