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Math & Teaching Intermediate

Combinatorics: Counting Principles, Permutations, Combinations & Probability

Multiplication principle, FACT, PERMUT, COMBIN, multinomials, inclusion–exclusion, stars and bars, Pascal's triangle and the birthday problem: 8 graded labs on passwords, teams, menus and lottery odds.

8 lessons 8 labs 1.9 h Certificate

  • One-time payment
  • 14-day money-back guarantee
  • Secure checkout with Stripe

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

  • Count kit outfits, locker codes and menu combinations at a sports club, and see why codes get safer so fast.
  • Count relay line-ups, round-table seatings and app passwords, then find how many passwords repeat a character.
  • Count committees, committees with a quota, ice-cream cups with repeated flavours and pizza topping choices.
  • Count flag orders with repeated colours, split volunteers into job teams and count shortest walking routes on a grid.
  • Count members in overlapping activities, use the three-set formula and count passwords that need a letter and a digit.
  • Count ways to share identical vouchers, bagels and hours, with and without a minimum, and handle an upper limit with inclusion–exclusion.
  • Build Pascal's triangle with COMBIN, discover the row sums and use a coefficient for a free-throw probability.
  • Compute the birthday probability for groups of 5 to 70, chart it, and work out jackpot and 3-match odds in a 6-from-49 club lotto.

About this course

How many passwords, teams or lottery tickets are possible? Counting questions like these underpin probability, and this course teaches the techniques behind them. You start with the multiplication principle for outfits, codes and menus, then count permutations with and without repetition and combinations and subsets. Multinomial coefficients handle arrangements with identical items, and inclusion-exclusion counts overlapping sets correctly. Stars and bars distributes identical items into groups. You build Pascal's triangle and use binomial coefficients for binomial probability, and finish with the birthday problem and lottery odds. Ideal for maths students, exam candidates, teachers and puzzle lovers.

Curriculum

Course content

8 lessons · 8 labs · 1.9 h · final exam

  1. The Multiplication Principle: Outfits, Codes & MenusLab12 min3 checked tasks
    Unlocked when you buy the course
  2. Permutations: FACT, PERMUT & RepetitionLab14 min4 checked tasks
    Unlocked when you buy the course
  3. Combinations: COMBIN, COMBINA & SubsetsLab14 min4 checked tasks
    Unlocked when you buy the course
  4. Arrangements with Identical Items: the MultinomialLab14 min4 checked tasks
    Unlocked when you buy the course
  5. Inclusion–Exclusion: Counting OverlapsLab14 min4 checked tasks
    Unlocked when you buy the course
  6. Stars and Bars: Distributing Identical ItemsLab15 min3 checked tasks
    Unlocked when you buy the course
  7. Binomial Coefficients, Pascal's Triangle & Binomial ProbabilityLab16 min4 checked tasks
    Unlocked when you buy the course
  8. The Birthday Problem & Lottery OddsLab16 min4 checked tasks
    Unlocked when you buy the course
  9. Final exam12 questions, 75% to pass, unlimited retries.

Certificate

Finish with a certificate you can verify

Complete every lesson and pass the final exam to receive a certificate of completion for this course, with a unique credential ID and a public verification page.

  • Names the course, your score and the date of issue
  • A verification link for your CV or LinkedIn profile
  • 12 questions, 75% to pass, unlimited retries.

A Tutorvo certificate confirms that you completed a course. It is not an official or professional qualification.

Illustration. Your certificate shows your own name, course and credential ID.

Before you buy

Questions about this course

Is this a subscription?

No. You pay $9.99 once for this course. There is no subscription and nothing renews automatically. Prices are in US dollars; taxes may be added where required.

What exactly do I get?

All lessons and labs of this course, the final exam and the certificate, including later updates to the course, for as long as Tutorvo offers it. Access is personal and tied to your account.

Can I get a refund?

Yes. If you are not satisfied, email hello@tutorvo.com within 14 days of buying and we refund the course in full via Stripe. The guarantee does not apply once a certificate for the course has been issued to you, or where there are signs of abuse.

When can I start?

Right after payment. Access starts immediately at your request; for consumers in the EU/EEA the statutory right of withdrawal therefore ends once access has begun, while our 14-day money-back guarantee applies regardless.

Do I need Excel or other software?

No. The labs run in a spreadsheet inside your browser on a laptop, tablet or phone. Function names and syntax follow Excel.

Is the certificate an official qualification?

No. It confirms that you completed all lessons of the course and passed its final exam. It is not an official, state-recognised or professional qualification. The name is taken from your profile when the certificate is issued.

Full details are in our Terms · hello@tutorvo.com

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