Question
Given a set of 8 elements, evaluate $\mathrm{nPr}$ and $\mathrm{nCr}$ for creating a subset of 4 elements.
Provide your answer below:
\[
P(n, r)=70
\]
\[
C(n, r)=70
\]
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Answer
Final Answer: The number of permutations of a set of 8 elements taken 4 at a time is \(\boxed{1680}\) and the number of combinations is \(\boxed{70}\).
Step 1 ：The problem is asking for the number of permutations and combinations of a set of 8 elements taken 4 at a time.
Step 2 ：For permutations, the formula is \(\mathrm{nPr} = \frac{n!}{(n-r)!}\) where n is the total number of elements and r is the number of elements to select.
Step 3 ：For combinations, the formula is \(\mathrm{nCr} = \frac{n!}{r!(n-r)!}\) where n is the total number of elements and r is the number of elements to select.
Step 4 ：Let's calculate these values. Given n = 8 and r = 4, we find that \(\mathrm{nPr} = 1680.0\) and \(\mathrm{nCr} = 70.0\).
Step 5 ：Final Answer: The number of permutations of a set of 8 elements taken 4 at a time is \(\boxed{1680}\) and the number of combinations is \(\boxed{70}\).
