In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?Choices:- 360 480 720 800
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?
Choices:
- 360
- 480
- 720
- 800
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.
5! = 5 * 4 * 3 * 2 * 1 = 120
Next, within the 'vowel group' of EA and I, we have 3! (3 factorial) ways to arrange these.
3! = 3 * 2 * 1 = 6
So, the total number of ways to arrange the letters of the word 'LEADING' such that the vowels always come together is 120 * 6 = 720.
Therefore, the correct answer is 720.
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