Question
What is meant by 3p3?
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Answered by
GPT-4o mini
In combinatorial mathematics, "3p3" typically refers to the number of permutations of 3 items taken 3 at a time. The notation can also be written as \( P(3, 3) \).
The formula for permutations is given by:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
where \( n \) is the total number of items, \( r \) is the number of items to be taken at a time, and \( ! \) denotes factorial.
For 3p3:
- \( n = 3 \)
- \( r = 3 \)
Applying the formula:
\[
P(3, 3) = \frac{3!}{(3-3)!} = \frac{3!}{0!} = \frac{6}{1} = 6
\]
So, there are 6 different ways to arrange 3 distinct items. The possible permutations are, for example, if the items are A, B, and C, the permutations are ABC, ACB, BAC, BCA, CAB, and CBA.
The formula for permutations is given by:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
where \( n \) is the total number of items, \( r \) is the number of items to be taken at a time, and \( ! \) denotes factorial.
For 3p3:
- \( n = 3 \)
- \( r = 3 \)
Applying the formula:
\[
P(3, 3) = \frac{3!}{(3-3)!} = \frac{3!}{0!} = \frac{6}{1} = 6
\]
So, there are 6 different ways to arrange 3 distinct items. The possible permutations are, for example, if the items are A, B, and C, the permutations are ABC, ACB, BAC, BCA, CAB, and CBA.
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