Find the number of distinguishable permutations of the following letters:
M, I, S, S, I, S, S, I, P, P, I.
4 S's
2 P's
4 I's
number of permutations
= 11!/(4!4!2!)
= 34650
To find the number of distinguishable permutations of the given set of letters, you can follow these steps:
Step 1: Determine the total number of letters in the set.
In this case, the set consists of 11 letters: M, I, S, S, I, S, S, I, P, P, I.
Step 2: Determine the number of repetitions for each letter.
Count the number of times each letter appears in the set:
- M appears 1 time
- I appears 4 times
- S appears 3 times
- P appears 2 times
Step 3: Apply the permutation formula.
The formula for finding the number of permutations of a set with repeated elements is:
N! / (n1! * n2! * n3! * ... * nk!)
Where:
- N is the total number of elements in the set (11 in this case)
- n1, n2, n3, ... nk are the number of repetitions for each distinct element
Step 4: Plug the values into the formula and calculate.
Using the values from Step 2, we have:
11! / (1! * 4! * 3! * 2!)
= 11! / (1 * 4 * 3 * 2)
To simplify the calculation, you can cancel out common factors:
= (11 * 10 * 9 * 8 * 7 * 6 * 5) / (4 * 3 * 2)
= (11 * 10 * 9 * 7 * 5) / (2)
= 11 * 10 * 9 * 7 * 5
= 34,650
Therefore, the number of distinguishable permutations of the letters "MISSISSIPPI" is 34,650.