Question

In how many ways can the letters of the word COTTON be arranged so that the two T's
are not together?
O A) 180
OE) 80
OC) 120
OD 100​

Answer 1

Answer:

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Answer 2

Concept: Permutation Combination.
Given: To find in how many ways can the letters of the word COTTON be arranged so that the two T's won't come together.
Answer: 120
Explanation:
Cotton word has 2T's.
The formula =
(n! / p! r!) where,
n = no. of total letters in a word
p = no. of repeating letter of one type
r = no. of repeating letter of another type
So ( 6!/2!*2!) = 180
Now let us consider 2 T's as one then we have total five letters which can be arranged in
(5!/2!) = 60
Hence, the no. of ways in which T’s will never come together = (Total number of arrangements-Total no. of arrangements in which T’s are together)
= 180–60 = 120
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