Permutation
Calculate permutations in Grade 9 math using the formula nPr=n!/(n-r)! to count ordered arrangements of r items chosen from n, where every different sequence is counted separately.
Key Concepts
Property The number of permutations of $n$ objects taken $r$ at a time is given by the formula $ nP r = \frac{n!}{(n r)!}$. Explanation Permutations are for when order is king, like winning 1st, 2nd, and 3rd place in a race. You have a big group of 'n' things, but you're only picking and arranging 'r' of them. This formula is your secret weapon to calculate all possible ordered arrangements without having to list them all out one by one. Examples In a race with 8 runners, the number of ways to award gold, silver, and bronze medals is $ 8P 3 = \frac{8!}{(8 3)!} = \frac{8!}{5!} = 336$. From a team of 10 players, the number of ways to pick a captain and a vice captain is $ {10}P 2 = \frac{10!}{(10 2)!} = \frac{10!}{8!} = 90$. The number of ways 5 different books can be arranged on a shelf is $ 5P 5 = \frac{5!}{(5 5)!} = \frac{5!}{0!} = 120$.
Common Questions
What is a permutation in mathematics?
A permutation is an ordered arrangement of objects. The order matters, so ABC and BAC are counted as different permutations. The formula is nPr = n! / (n-r)!, giving the number of ways to choose and arrange r items from n total.
How do you calculate 7P3 (permutations of 7 items taken 3 at a time)?
Apply the formula: 7P3 = 7! / (7-3)! = 7! / 4! = (7 × 6 × 5 × 4!) / 4! = 7 × 6 × 5 = 210. There are 210 ordered arrangements of 3 items selected from 7.
What does n! (n factorial) mean and how is it calculated?
n factorial is the product of all positive integers from 1 to n. So 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. Factorials grow very quickly: 10! = 3,628,800.