Question

How many different 11-letter words (real or imaginary) can be formed from the letters in the word PROBABILITY?

Answer 1

Answer:  9,979,200

This is one single number. It's just a bit under 10 million

Delete the commas if necessary.

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Explanation:

If we could tell the repeated letters apart, then there would be

11*10*9*8*7*6*5*4*3*2*1 = 39,916,800

different ways to scramble up the letters.

However, we have 2 copies of b and 2 copies of i

So we have to divide by 2*2 = 4 to correct this overcounting

(39,916,800)/4 = 9,979,200