find the number of ways of arranging all the letters of the word PACIFIC in how many of them
1 . the two C come together
2. the two I's do not come together
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Question ⤵️
Find the number of ways of permuting the letters of the word PICTURE so that
(i) All vowels come together
(ii) No two vowels come together
(iii) The relative positions of vowels and consonants are not disturbed
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ANSWER
Answer ⤵️
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:
1 - 360
2 - 360
Step-by-step explanation:
number of letter in word PACIFIC = 7
Let's take the 2c's as one since they have to be next to each other so
6! / 2! (there is a 2! because I is repeating) = 360
same goes for the 2nd sub divisions take the I as one block and divide by 2 since C is repeating
hope this helps