Problem 368 Calculate the number of permutat... [FREE SOLUTION]

Chapter 7: Problem 368

Calculate the number of permutations of the letters \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) taken four at a time.

Short Answer

Expert verified

There are 24 different permutations of the letters a, b, c, and d taken four at a time.

Step by step solution

Understand Permutations and the Permutation Formula

Permutations refer to arrangements of items in a specific order. The permutation formula for arranging n objects in r different ways is given by: \[P(n,r) = \frac{n!}{(n-r)!}\] where n! denotes the factorial of n. The factorial function, n! = n*(n-1)*(n-2)*...*1.

Identify the number of items and how many at a time

In this exercise, we have 4 distinct letters (a, b, c, and d) and we want to find the permutations when selecting 4 at a time. Therefore, we have n=4 and r=4.

Apply the Permutation Formula

Plugging the values of n and r into the permutation formula, we get: \[P(4,4) = \frac{4!}{(4-4)!}\]

Simplify and Calculate the Permutations

Let's simplify the equation and calculate the permutations: \[P(4,4) = \frac{4!}{0!}\] Here, we should note that 0! is always equal to 1. Therefore, \[P(4,4) = \frac{4!}{1} = 4!\] Now calculate 4!: \[4! = 4\times 3\times 2\times 1 = 24\] So, there are 24 different permutations of the letters a, b, c, and d taken four at a time.

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91影视

Calculate the number of permutations of the letters \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) taken four at a time.

Short Answer

Step by step solution

Understand Permutations and the Permutation Formula

Identify the number of items and how many at a time

Apply the Permutation Formula

Simplify and Calculate the Permutations

One App. One Place for Learning.

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