Consider the letters in the word SAMPLE. In how many ways can you arrange 5 of the letters?There are ways to arrange 5 of the letters.
Question
Consider the letters in the word SAMPLE.
In how many ways can you arrange 5 of the letters?
There are ways to arrange 5 of the letters.
Solution
The word "SAMPLE" has 6 distinct letters. If we want to arrange 5 of these letters, we can use the formula for permutations of a multiset:
P(n, r) = n! / (n-r)!
where n is the total number of items, r is the number of items to choose, and "!" denotes factorial, which is the product of all positive integers up to that number.
Here, n = 6 (the letters in "SAMPLE") and r = 5 (the number of letters we want to arrange).
So, we have:
P(6, 5) = 6! / (6-5)!
= 720 / 1
= 720
So, there are 720 ways to arrange 5 of the letters in "SAMPLE".
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