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If the letters of the word 'MINIMUM' are arranged in a line at random, what is the probability that the 3 M's are together at the beginning of the arrangement.

There are 2 methods outlined to solve this problem.

Method 1: (3/7)*(2/6)*(1/5)=(1/35) I understand this method completely.

The method I would like clarified is:

Method 2:

The statistical weight, w, w=7!/(3!2!1!1!)=420.

The number of ways of writing 'mmm****' where * is (i,n,u) is 4!/(2!1!1!)=12.

Thus p=12/420=1/35

I get that the factorials are used as m is repeated 3 times, and i 2 times. I don't know why we divide by these, as in my mind there are 7! possible ways of arranging the letters, albeit some of them repeats. For probability, why is this used? Thanks

There are 2 methods outlined to solve this problem.

Method 1: (3/7)*(2/6)*(1/5)=(1/35) I understand this method completely.

The method I would like clarified is:

Method 2:

The statistical weight, w, w=7!/(3!2!1!1!)=420.

The number of ways of writing 'mmm****' where * is (i,n,u) is 4!/(2!1!1!)=12.

Thus p=12/420=1/35

I get that the factorials are used as m is repeated 3 times, and i 2 times. I don't know why we divide by these, as in my mind there are 7! possible ways of arranging the letters, albeit some of them repeats. For probability, why is this used? Thanks

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