How many words can be formed using all the letters MMONDAAYTREEWE?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The number of ways in which r out of n different objects can be re-arranged or the number of permutations of r objects chosen from a set of n different objects is given by nPr = `(n!)/((n-r)!)` .

Here, the number of words that can be formed using all the letters MMONDAAYTREEWE has to be determined.

The total number of letters of 14, but they are not unique. There are 2 letters M, 2 letters A and 3 letters E.

To determine the number of words that can be formed, the value of nPr has to be divided by the factorial of the number of times each of any object is repeated.

Also, as all the letters have to be used r = n.

That gives: `(14P14)/(2!*3!*2!)`

=> `(14!)/((14-14)!2!*3!*2!)`

The required number of words that can be formed using the given letters is `(14!)/(2!*3!*2!)` .

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