Question

In how many ways can the letters in mmm ppq can be arranged with two n's together

Answer 1

15120 ways can be arranged

Answer 2

Thank you for asking this question. Here is your answer:

Arranging with 2 n’s together:

Select 2 n’s out of three = 3C2 = 3

The selected 2 n’s are considered as one.

There will be 9 elements after combining.

Number of arrangements,

= [9!/(3! x 2! x 2!)] x (2!/2!) x 3

= 11340

In the above arrangements, some them will have 3 n’s together.

Now we will eliminate these:

Number of arrangements in which 3 n’s are together, = [8!/(3! x 2! x 2!)](3!3!)

= 420

Number of arrangements in which 2 n’s are together,

= 11340 – 420 = 10920

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