Question

From the word 'propriety', how do you find all the possible words / different arrangements of all the letters? (answer is 90720)

Answer 1

`90720`

Explanation:

P.R.O.P.R.I.E.T.Y

There are `7` distinct letters in this word, of which `2` ( P and R ) are repeated twice.

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Method 1:

Figure out how many ways the two P's can be placed,

`9C2`

Figure out how many ways the two R's can be placed,

`7C2`

Figure out how many ways the individual letters can be placed,

`5!`

Multiply them all up,

`9C2*7C2*5! =90720`

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Method 2:

Figure out how many ways the word could be rearranged supposing all letters are distinct,

`9!`

Since there are `2` duplicates, divide them out,

`(9!)/(2!*2!)=90720`