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  • In how many ways can the letters of the word "SUCCESS" be arranged if the two C’s are never together?  Option: 1 1170<

In how many ways can the letters of the word "SUCCESS" be arranged if the two C’s are never together?

 

Option: 1

1170


Option: 2

2160


Option: 3

3180


Option: 4

4230


Answers (1)

best_answer

There are seven letters in the word "SUCCESS", but the two C’s cannot be together. 

We can solve this problem using complementary counting. 

First, we find the total number of permutations of the letters of "SUCCESS", which is given by,

\frac{7 !}{2 ! 2 !}=2520

Next, we find the number of permutations where the two C’s are together. We can treat the two C’s as a single object, which can be arranged in 6 ways. 

Then we can arrange the remaining 5 letters in 5! ways. Therefore, the number of permutations where the two C’s are together is given by

\frac{6 \times 5 !}{2 ! 2 !}=360

Finally, we subtract the number of permutations where the two C’s are together from the total number of permutations to get:


2520-360=2160

Therefore, there are 2,160 ways to arrange the letters of "SUCCESS" such that the two Cs are never together.

 

 

Posted by

Rakesh

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