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Counting: permutations and combinationsStatistics and probabilityHigh schoolabout 0:35

How many ways can you arrange 2 of 12 items in order?: animated lesson

A narrated, step-by-step counting: permutations and combinations video lesson with captions. Final answer: P(12, 2) = 132.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
How many ways can you arrange 2 of 12 items in order?
2. Step by step
1. $P(12, 2) = \frac{12!}{(12 - 2)!} = \frac{12!}{10!}$
  Use the permutation formula
2. $12 \times 11 = 132$
  Cancel 10! to leave the first 2 factors of 12!
3. The answer
$132$
132
4. Check
- Check: P(12, 2) = C(12, 2) × 2! = 66 × 2 = 132.

Transcript

The problem. Here is the problem: How many ways can you arrange 2 of 12 items in order? Permutations nPr (order matters).

Step by step. Use the permutation formula. Cancel 10! to leave the first 2 factors of 12!

The answer. So the answer is P(12, 2) equals 132. There are 132 ordered arrangements of 2 items chosen from 12.

Check. Check: P(12, 2) equals C(12, 2) times 2! equals 66 times 2 equals 132.

About counting: permutations and combinations

Count arrangements and selections with permutations and combinations.

How many ways can you arrange 2 of 12 items in order?