In how many different ways can the letters of the word SANTACLAUS be arranged?
I see 10 letters containing 3 A's and 2 S's.
So the number of arrangements is
10!/(3!2!) = .....
Thank you so much! :)
302,400
To find the number of different ways the letters of the word SANTACLAUS can be arranged, we can use the concept of permutations.
The formula to calculate permutations is:
nPr = n! / (n - r)!
Where n represents the total number of items and r represents the number of items taken at a time.
In this case, we have the word SANTACLAUS, which consists of 11 letters (n = 11). We want to arrange all the letters, so r = 11.
Plugging in these values into the permutation formula, we get:
11P11 = 11! / (11 - 11)!
= 11! / 0!
= 11! / 1
= 11!
Since 0! is equal to 1, we can simplify the expression:
11P11 = 11!
To find the value of 11!, we multiply all the integers from 1 to 11:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 39,916,800
So, there are 39,916,800 different ways to arrange the letters of the word SANTACLAUS.