Textbook Question
Use the formula for nCr to evaluate each expression. 5C0
676
views
2
rank
10. Combinatorics & Probability
Combinatorics
2:08 minutesProblem 5
Textbook Question
Use the formula for nPr to evaluate each expression. 6P6
Verified step by step guidance1
Recall the formula for permutations: \(nP_r = \frac{n!}{(n-r)!}\), where \(n\) is the total number of items and \(r\) is the number of items to arrange.
Identify the values of \(n\) and \(r\) in the expression \$6P6\(. Here, \)n = 6\( and \)r = 6$.
Substitute these values into the formula: \(6P6 = \frac{6!}{(6-6)!}\).
Simplify the denominator: \((6-6)! = 0!\). Remember that by definition, \$0! = 1$.
The expression now becomes \(6P6 = \frac{6!}{1} = 6!\). To find the value, you would calculate \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\), but the problem only asks for the setup.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Permutation Formula (nPr)
The permutation formula nPr calculates the number of ways to arrange r objects from a set of n distinct objects, where order matters. It is given by nPr = n! / (n - r)!, where '!' denotes factorial.
Recommended video:
7:11
Introduction to Permutations
Factorial Notation
Factorial, denoted by n!, is the product of all positive integers from 1 up to n. For example, 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. Factorials are essential in permutations and combinations calculations.
Recommended video:
5:22Factorials
Evaluating nPr When r = n
When the number of objects chosen r equals the total number n, nPr simplifies to n!, because (n - n)! = 0! = 1. Thus, nPn = n!, representing all possible arrangements of the entire set.
Recommended video:
5:22Combinations
Related Videos
Related Practice