Periorm the indicated calculation. \( { }_{6} P_{4} \)
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To calculate \( { }_{6} P_{4} \), which represents the number of permutations of 4 items selected from a set of 6, you can use the formula: \[ _{n}P_{r} = \frac{n!}{(n - r)!} \] Plugging in our values \( n = 6 \) and \( r = 4 \): \[ _{6}P_{4} = \frac{6!}{(6 - 4)!} = \frac{6!}{2!} = \frac{720}{2} = 360 \] So, \( { }_{6} P_{4} = 360 \). Get ready to impress your friends with this! Permutations are like arranging apples in different baskets; the order matters. In this case, you can arrange 4 apples chosen from 6 in a whopping 360 unique ways! It’s a fun way to think about how choices can multiply into a multitude of possibilities. If you’re curious about more complex permutations, consider diving into topics like combinations and factorials. They can add depth to your understanding of probability and statistics! You’ll see just how fascinating the world of mathematics can be when you explore these areas further.