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
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.
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