courses › Counting & Discrete Math

Multiply choices, arrange things in order, handle repeats.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 15.

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Builds on: Bigger multiplication (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Multiply the choices par 13 s not tried yet

  worked example

  A café offers 7 starters and 7 main courses. How many different meals with one of each can you order?

  Answer: 49

  1. Each choice multiplies the options: 7 × 7 = 49.

• Factorial ratios par 8 s not tried yet

  worked example

  What is 6! ÷ 3!?

  Answer: 120

  1. Everything from 3 down cancels, leaving 6 × 5 × 4 = 120.

• Ordered picks par 18 s not tried yet

  worked example

  6 runners race. In how many ways can first place and second place be awarded, with no ties?

  Answer: 30

  1. 6 choices for first place and 5 choices for second place: order matters, so multiply.
  2. 6 × 5 = 30.

• Arrangements with repeats par 20 s not tried yet

  worked example

  How many different arrangements are there of the letters in LITTLE?

  Answer: 180

  1. 6! = 720 orders, but rearranging the two Ls or the two Ts among themselves gives the same word.
  2. 720 ÷ (2! × 2!) = 720 ÷ 4 = 180.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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