In how many different ways can the letters of the word UPGRAD be arranged so that be the vowels never come together?Answer( Please choose a correct answer ) CLEAR360720540480
Question
In how many different ways can the letters of the word UPGRAD be arranged so that be the vowels never come together?Answer( Please choose a correct answer ) CLEAR360720540480
Solution
The total number of ways to arrange the letters in the word "UPGRAD" is 6! (6 factorial) because there are 6 letters. This equals 720 ways.
However, we need to subtract the cases where the vowels (U and A) are together. We can treat the vowels as a single entity (UA or AU), so we have 5 entities to arrange (UA, P, G, R, D), which is 5!. This equals 120 ways. But within these 120 ways, the two vowels can be arranged in 2! = 2 ways (UA or AU). So the total number of ways where the vowels are together is 120 * 2 = 240.
Therefore, the number of ways to arrange the letters so that the vowels never come together is 720 - 240 = 480. So, the correct answer is 480.
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