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In how many ways the word “PRIDE” be arranged so that all vowels and consonants come together?Choices:- 12 18 24 32

Question

In how many ways can the word “PRIDE” be arranged so that all vowels and consonants come together?

Choices:

  • 12
  • 18
  • 24
  • 32
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Solution

The word "PRIDE" has 2 vowels (I, E) and 3 consonants (P, R, D).

Step 1: Since all vowels and consonants must come together, we can treat the group of vowels as a single letter and the group of consonants as a single letter. So, we have two "letters" to arrange: V (vowels) and C (consonants).

Step 2: These two "letters" can be arranged in 2! = 2 ways.

Step 3: Within the vowels group, we have 2 vowels which can be arranged in 2! = 2 ways.

Step 4: Within the consonants group, we have 3 consonants which can be arranged in 3! = 6 ways.

Step 5: Multiply the number of arrangements for each group together to get the total number of arrangements.

So, the total number of ways = 2 (arrangements of V and C) * 2 (arrangements of vowels within V) * 6 (arrangements of consonants within C) = 24 ways.

So, the answer is 24.

This problem has been solved

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