Combinatorics quiz

More questions about Combinatorics

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   How many handshakes happen if 10 people all shake hands once?

   Answer: 45

   Why: Each person shakes 9 hands, but 10 × 9 = 90 counts every handshake twice, once from each side, so the real total is half of that.

2. 2 Medium

   Which group size first guarantees a shared birthday, counting 29 February?

   Answer: 367

   Why: With 23 people the chance is only about 50.7%; certainty takes one more person than the 366 possible birthdays.

3. 3 Hard

   What span of time equals exactly 10! seconds?

   Answer: 6 weeks

   Why: The numbers 2 to 10 regroup as 6 × 7 × (2 × 3 × 4) × (5 × 8 × 9 × 10): weeks, days per week, hours per day, seconds per hour.

4. 4 Easy

   How many matches find the winner of a 128-player knockout?

   Answer: 127

   Why: Every match knocks out one player and all but the champion must go, which is why rounds of 64, 32, 16, 8, 4, 2 and 1 matches add up to 127.

5. 5 Medium

   Which sequence counts ways to climb stairs taking 1 or 2 steps?

   Answer: Fibonacci numbers

   Why: Your last step comes from 1 or 2 stairs below, so each count is the sum of the two before it, and 10 stairs already allow 89 ways.

6. 6 Hard

   What is the number of zeros that 100! ends with?

   Answer: 24

   Why: Each zero needs a 2 × 5 pair and fives are scarcer: the 20 multiples of 5 give 20, and 25, 50, 75 and 100 each add a second five.