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Counting: permutations and combinationsStatistics and probabilityHigh schoolabout 0:34

How many ways can you choose 3 items from 10?: animated lesson

A narrated, step-by-step counting: permutations and combinations video lesson with captions. Final answer: C(10, 3) = 120.

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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 choose 3 items from 10?
2. Step by step
1. $C(10, 3) = \frac{10!}{3!\,7!}$
  Use the combination formula
2. $\frac{P(10, 3)}{3!} = \frac{720}{6} = 120$
  Divide the permutations by r! because order does not matter
3. The answer
$120$
120
4. Check
- Check: P(10, 3) = C(10, 3) × 3! = 120 × 6 = 720.

Transcript

The problem. Here is the problem: How many ways can you choose 3 items from 10? Combinations nCr (order does not matter).

Step by step. Use the combination formula. Divide the permutations by r! because order does not matter.

The answer. So the answer is C(10, 3) equals 120. There are 120 ways to choose 3 items from 10 when order does not matter.

Check. Check: P(10, 3) equals C(10, 3) times 3! equals 120 times 6 equals 720.

About counting: permutations and combinations

Count arrangements and selections with permutations and combinations.

How many ways can you choose 3 items from 10? (Lesson)