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Quiz: Counting

5 questionsNo time limitPass: 60%+10 XP on first pass

Count without listing: the sum and product rules, permutations and combinations (with and without repetition), arrangements with identical items, stars and bars, inclusion–exclusion and derangements — every formula checked by brute force in Python.

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  1. Question 1

    In how many ways can a captain and vice-captain be chosen from 11 players?

  2. Question 2

    How many distinct arrangements of the letters of BANANA are there?

  3. Question 3

    In how many ways can 10 identical chocolates be distributed among 3 children (some may get none)?

  4. Question 4

    How many numbers from 1 to 1000 are divisible by 2, 3 or 5 (from the demo)?

  5. Question 5

    What is D4, the number of derangements of 4 items?