SHSAT Math · Statistics & Probability
Combinatorics Practice
Counting principles, permutations, and combinations. This is one of the skills tested on the SHSAT; the 2026 exam is computer-based with 50 Math questions in a 90-minute section. Try the samples below, then practice the full topic with instant feedback and explanations.
Free sample questions
Question 1
At a meeting, each of people shakes hands exactly once with every other person. How many handshakes occur?
- A
- B
- C
- D
Show answer and explanation
Answer: B
Each pair shakes once: .
Question 2
At a meeting, each of people shakes hands exactly once with every other person. How many handshakes occur?
- A
- B
- C
- D
Show answer and explanation
Answer: A
Each pair shakes once: .
Question 3
A password has 4 letters followed by 8 digits. How many passwords are possible with repetition allowed?
- A131
- B65
- C262
- D139
Show answer and explanation
Answer: A
Using combinatorial principles, the answer is 131.
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