courses › Counting & Discrete Math

Choosing groups where order doesn’t matter.

Pen and paper is fine · no calculator needed why?

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Opens at level 25.

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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.

• Choose k of n par 15 s not tried yet

  worked example

  In how many ways can you choose 4 people from 11 for a team, if order doesn’t matter?

  Answer: 330

  1. C(11, 4) = (11 × 10 × 9 × 8) ÷ (4 × 3 × 2 × 1)
  2. = 7,920 ÷ 24 = 330.

• Committees par 25 s not tried yet

  worked example

  A squad needs 1 defender chosen from 4 and 2 forwards chosen from 5. How many different squads are possible?

  Answer: 40

  1. Choose each group separately, then multiply: every choice of defenders goes with every choice of forwards.
  2. C(4, 1) × C(5, 2) = 4 × 10 = 40.

• Grid paths par 20 s not tried yet

  worked example

  On a grid 6 blocks wide and 4 blocks tall, how many shortest paths go from the bottom-left corner to the top-right corner, moving only right or up?

  Answer: 210

  1. Every path is 10 moves: 6 right and 4 up. Choose which 6 of the 10 moves go right:
  2. C(10, 6) = 210.

• Sharing identical items par 30 s not tried yet

  worked example

  In how many ways can 7 identical cookies be shared among 4 children if each child gets at least one?

  Answer: 20

  1. Line up the 7 cookies. Put 3 dividers into the 6 gaps between them, at most one per gap, so no share is empty.
  2. C(6, 3) = 20.

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

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