Answer to Question #146450 in Combinatorics | Number Theory for Josh

Question #146450
Find the number of distinguishable permutations that can be formed from the letters of the word "CINCINNATI"
a.604800
b.25200
c.50400
d.100800
1
Expert's answer
2020-11-30T10:33:31-0500

"CINCINNATI: 2C, 3I, 3N, 1A,1T"

There are 10 letters in the word "CINCINNATI"

The number of permutations of 10 elements is given by the following formula:


"P_{10}=10!"

The letter "C" is repeated 2 times in the word.

The letter "I" is repeated 3 times in the word.

The letter "N" is repeated 3 times in the word.

The number of distinguishable permutations that can be formed from the letters of the word "CINCINNATI" is


"\\dfrac{10!}{2!\\cdot3!\\cdot3!}=\\dfrac{10(9)(8)(7)(6)(5)(4)(3)(2)(1)}{2\\cdot6\\cdot6}"

"=\\dfrac{3628800}{72}=50400"

c. 50400



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS