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Counting: permutations and combinationsStatistics and probabilityHigh schoolabout 0:37

How many ways can you arrange 3 of 8 items in order?: animated lesson

A narrated, step-by-step counting: permutations and combinations video lesson with captions. Final answer: P(8, 3) = 336.

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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 3 of 8 items in order?
2. Step by step
1. $P(8, 3) = \frac{8!}{(8 - 3)!} = \frac{8!}{5!}$
  Use the permutation formula
2. $8 \times 7 \times 6 = 336$
  Cancel 5! to leave the first 3 factors of 8!
3. The answer
$336$
336
4. Check
- Check: P(8, 3) = C(8, 3) × 3! = 56 × 6 = 336.

Transcript

The problem. Here is the problem: How many ways can you arrange 3 of 8 items in order? Permutations nPr (order matters).

Step by step. Use the permutation formula. Cancel 5! to leave the first 3 factors of 8!

The answer. So the answer is P(8, 3) equals 336. There are 336 ordered arrangements of 3 items chosen from 8.

Check. Check: P(8, 3) equals C(8, 3) times 3! equals 56 times 6 equals 336.

About counting: permutations and combinations

Count arrangements and selections with permutations and combinations.

How many ways can you arrange 3 of 8 items in order?