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Exercises Sequences, counting and probability

Example 7 from Algebra and Trigonometry, 13.5 Counting Principles

Finding the Number of Permutations of n Non-Distinct Objects

Find the number of rearrangements of the letters in the word DISTINCT.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
There are 8 letters. Both I and T are repeated 2 times. Substitute $n = 8, r_{1} = 2,$ and $r_{2} = 2$ into the formula.

$\frac{8!}{2! 2!} = 10, 080$
There are 10,080 arrangements.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the number of rearrangements of the letters in the word CARRIER.

How did it go?

PreviousFinding the Number of Subsets of a Set Next Finding Binomial Coefficients

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 13.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.