raman classes test series

Question

number of ways of arranging the letters GGGGGAAATTTECCS such that no two T's are together?

Comments

@ank73811 even i was getting the same but it is not matching with any option,

@Magma @MiNiPandacan u pls explain how b??thats correct answer!

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@Gate Fever

Option C means 3 T's won't be together. But you didn't consider the case when 2 T's are together. You have to subtract that also.

Else take a different approach..

Keeping the 3 T's away for now, no. of ways to arrange the rest is

5Gs,3As,2Cs,1E,1S ---> $\frac{12!}{5!3!2!}$

Now to keep the T's separated from each other we need to place them in b/w the gaps of these 12 alphabets. There are 13 gaps. We choose 3 of them in C(13,3) ways. C(13,3)=P(13,3)/3!

So, $\frac{12!}{5!3!2!} \times \frac{P(13,3)}{3!}$

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thanks!