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Find the number of ways of arranging the letters of PROBABILITY.

 Jun 10, 2020
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PROBABILITY has 11 letters.

 

The most straightforward thought would be the factorial of 11. But there are repeating letters, so we would have double-counted if we say the number of ways is 11!.

 

In fact, we need to divide by the factorial of the number of each type of repeating letters.

 

The number of ways would be \(\dfrac{11!}{\color{green}2!\color{blue}2!\color{black}} = 9979200\)

 

The green one is for repeating 'B's, and the blue one is for repeating 'I's.

 Jun 11, 2020

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