Permute and Combine!
Probability
Level
3
The number of ways in which the words that can be made with the letters of the word PLATE so that there are exactly two letters between two vowels is?
The answer is 24.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let us keep the first place for a Vowel.So,now the next Vowel Would be in the 4th Place.Hence,It would be arranged in 2! ways and the consonants would be done in 3! ways.Now,at next we would have 2nd and 5th place for Vowels(permuted in 2! ways) and 3! ways to arrange consonants.So total number of words=2X3!X2=24