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QUESTION

# How many distinguishable ways can the letter of the word SASSAFRAS be arranged using all the letters?

In a word where no letters are repeated, such as FRANCE, the number of distinguishable ways of arranging the letters could be calculated by 5!, which gives 120. However, when letters are repeated, you must use the formula (n!)/((n_1!)(n_2!)...)

There are 4 s's, 3 a's and a total of 9 letters.

(9!)/((4!)(3!))

= 362880/(24 xx 6)

= 2520

There are 2520 distinguishable ways of arranging the letters.

Practice exercises:

1. Find the number of distinguishable ways of arranging the letters in the word EXERCISES.

2. Find the number of distinguishable ways of arranging letters in the word AARDVARK.

Good luck!