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Counting: permutations and combinationsStatistics and probabilityHigh schoolabout 0:36

How many ways can you arrange 4 of 10 items in order?: animated lesson

A narrated, step-by-step counting: permutations and combinations video lesson with captions. Final answer: P(10, 4) = 5,040.

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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 4 of 10 items in order?
2. Step by step
1. $P(10, 4) = \frac{10!}{(10 - 4)!} = \frac{10!}{6!}$
  Use the permutation formula
2. $10 \times 9 \times 8 \times 7 = 5{,}040$
  Cancel 6! to leave the first 4 factors of 10!
3. The answer
$5{,}040$
5,040
4. Check
- Check: P(10, 4) = C(10, 4) × 4! = 210 × 24 = 5,040.

Transcript

The problem. Here is the problem: How many ways can you arrange 4 of 10 items in order? Permutations nPr (order matters).

Step by step. Use the permutation formula. Cancel 6! to leave the first 4 factors of 10!

The answer. So the answer is P(10, 4) equals 5,040. There are 5,040 ordered arrangements of 4 items chosen from 10.

Check. Check: P(10, 4) equals C(10, 4) times 4! equals 210 times 24 equals 5,040.

About counting: permutations and combinations

Count arrangements and selections with permutations and combinations.

How many ways can you arrange 4 of 10 items in order?