Question

In how many different ways apple can be arranged such that vowels come together

Answer 1

Answer:

So word APPLE contains 1A, 2P, 1L and 1E

Required number =

\begin{aligned}

= \frac{5!}{1!*2!*1!*1!} \\

= \frac{5*4*3*2!}{2!} \\

= 60

Answer: 60 different ways.

Answer 2

The number of ways in which apple can be arranged such that vowels come together is equal to 48 ways.

Explanation:

According to the given information, we are given the word apple and we need to find the many different ways apple can be arranged such that vowels come together.

Vowels in the English alphabet series start from a, then we have the letter e, then we have the letter i, then we have the letter o, and finally we have the letter u.

Therefore, there are only two vowels in the given word apple that is a and e.

Now, let us consider the vowels as one single unit.

Then, there are four units in the word to permute among themselves.

Also, the vowels in the vowel unit can interchange their positions.

Then, the number of ways in which apple can be arranged such that vowels come together is equal to (4! * 2!) ways.

Thus, we have, (4! * 2!) = 4*3*2*1*2*1 = 48 different ways.

Thus, the number of ways in which apple can be arranged such that vowels come together is equal to 48 ways.

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