Permutations of distinct objects
Count ordered arrangements of r objects chosen from n distinct objects using permutations, P(n, r). Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
There are 7 runners in a race. In how many different ways can the top 3 finishers (1st through 3rd) be arranged?
P(7, 3) = 7! / (7 - 3)!
Answer: 210
See one solved, step by step
There are 9 runners in a race. In how many different ways can the top 2 finishers (1st through 2nd) be arranged?
P(9, 2) = 9! / (9 - 2)!
📘 Worked solution
1P(9, 2) = 9 · 8Start at 9 and count down, using 2 factors -- one for each position being filled in order.
2= 72Multiply those 2 factors together.
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