Find the best answers to your questions with the help of IDNLearn.com's expert contributors. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Answer:
There are 2,520 unique permutations.
Step-by-step explanation:
When we have a set of N different elements, the total number of permutations is given by:
P = N! = N*(N - 1)*(N - 2)*...*(2)*(1)
Particularly, if out of these N elements, there are a given element that is repeated K times, then the permutations of these K elements actually do not add new unique permutations, then in that case the total number of unique permutations is:
P = N!/K!
And if we have another element that is repeated L times, then with the same reasoning than above, the total number of unique permutations is:
P = N!/(K!*L!)
Now, we have the set:
{C, E, A, S, E, L, E, S, S}
So we have a set of 9 letters, then:
N = 9
And, the letter S is repeated 3 times
The letter E is repeated 3 times
Then, using the above notation, we can define:
K = 3
L = 3
The total number of permutations is then:
[tex]P = \frac{9!}{3!*3!} = \frac{9*8*7*6*5*4*3*2*1}{3*2*1*3*2*1} = \frac{9*8*7*6*5*4}{3*2*1} = 2,520[/tex]
So there are 2,520 unique permutations.