What is \( { }_{6} P_{4} \) ? 15 0 24 360 720

To find \( { }_{6} P_{4} \), which stands for "6 permute 4," we use the formula for permutations: \[ { }_{n} P_{r} = \frac{n!}{(n-r)!} \] For \( { }_{6} P_{4} \): \[ { }_{6} P_{4} = \frac{6!}{(6-4)!} = \frac{6!}{2!} = \frac{720}{2} = 360 \] So, the answer is **360**. Permutations are all about arranging goodies! For example, if you have 6 different flavors of ice cream and you want to create a sundae with 4 scoops, the order matters. Since each flavor can only be used once per sundae, there are 360 unique combinations you could create. To avoid common mistakes with permutations like confusing them with combinations, remember: in permutations, the order of selection DOES matter! So, keep it straight: for \( { }_{n} P_{r} \), think "permutations," "order," and "factorials."