Find the number of permutations of the letters of the word COMPETITION so that vowels always occurctogether
Answers
Step-by-step explanation:
ANSWER
Rearrange the word PICTURE as PCTRIUE
i)
To keep the vowels together consider IUE as a single unit and the no. of permutation in IUE is 3!
total units become P,C,T,R,IUE = 5
so permutations will be 5!
so total permutations will be 5!*3!
ii)
No two vowels should be together so GIVE GAPS around them like I_U_E
Permutate IUE in 3! ways.
we need two fill in that we will choose from remaining in 4C2 ways
and will consider the selected two and IUE as a single unit and arrange with the remaining 2, so arranging three units is 3!ways
so total ways are - 5C2*3!*3! = 5!*3 = 360ways.
iii)
The relative position is not altered so we need to arrange 3 vowels in 3! ways and 4 consonants in 4! ways give total to be
4!*3!
Answer:
In the word mixture, consider the vowels i,u,e as one letter.
We have mxtr(iue).
The word has 5 letter.And 5 letters can be arranged in 5! ways.
Now three vowels can be arranged in 3! ways.
The required number of ways are = 5! * 3!
= 120 * 6
= 720.
{{You can take help of this question frm above answer.!!!}}