In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?Question 9Answera.40000b.4150c.50400d.3500
Question
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?Question 9Answera.40000b.4150c.50400d.3500
Solution
To solve this problem, we first consider the vowels (O,O,A,I,O) in the word 'CORPORATION' as a single letter.
So, we have the letters C, R, P, R, T, N, and (OOAIO) to arrange, which are 7 letters in total.
Since R and O are repeated, the number of ways to arrange these 7 letters is 7!/(2!*2!) = 1260 ways.
Next, we consider the vowels OOAIO. There are 5 vowels, with O being repeated 3 times.
The number of ways to arrange these 5 vowels is 5!/3! = 20 ways.
Therefore, the total number of ways to arrange the word 'CORPORATION' such that all vowels always come together is 1260 * 20 = 25200 ways.
So, none of the options a.40000, b.4150, c.50400, d.3500 is correct. The correct answer is 25200.
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