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Permutations and combinations worksheets

Whether order matters is a question about the story, not about the numbers. These free printable worksheets mix permutations and combinations so a student has to decide first and count second, with an answer sheet.

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Permutations and combinations
Permutations and combinations worksheet — Decide if order matters, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Three students getting three different medals is not the same as three students making a team. Gold, silver and bronze are different prizes, so swapping two winners gives a new outcome. A team is just the people on it, so swapping does nothing. The same numbers can give two very different answers, and only the wording says which.

Why this sheet works

The stories are written to make that decision fair. When order matters, the sentence names roles or places. When it does not, the sentence names a group. The notation nPr and nCr is left out, because here the method matters more than the symbol and a student can work every question by multiplying.

How this one works

A team of 3 is chosen from 7 students. How many different teams are possible?

765
7 × 6 × 5=210
210÷6=35
  1. Start as if order mattered. There are 7 choices for the first place, then 6 for the next, and so on for 3 places.
  2. 7 × 6 × 5 = 210.
  3. But a group has no first or second. The same 3 can be ordered in 3 × 2 × 1 = 6 ways, and all of those are one group. So divide: 210 ÷ 6 = 35.

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