Percy has 4 plots of soil in his backyard, and he wants to fill each one with a different type of flower. If the garden supply store has 5 types of flowers to choose from, in how many ways can he plant the plots?
Question
Percy has 4 plots of soil in his backyard, and he wants to fill each one with a different type of flower. If the garden supply store has 5 types of flowers to choose from, in how many ways can he plant the plots?
Solution
This is a problem of permutations without repetition.
Step 1: Identify the number of items to choose from and the number of choices to make. Here, Percy has 5 types of flowers to choose from and he needs to choose 4 for his plots.
Step 2: Use the formula for permutations without repetition, which is nPr = n! / (n - r)!. Here, n is the number of items to choose from (5 flowers) and r is the number of choices to make (4 plots).
Step 3: Calculate the factorial of n, which is n! = n * (n - 1) * (n - 2) * ... * 1. So, 5! = 5 * 4 * 3 * 2 * 1 = 120.
Step 4: Calculate the factorial of (n - r), which is (n - r)! = (n - r) * ((n - r) - 1) * ... * 1. So, (5 - 4)! = 1.
Step 5: Divide the factorial of n by the factorial of (n - r) to get the number of permutations. So, 120 / 1 = 120.
Therefore, Percy can plant the plots in 120 different ways.
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