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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 2424 people shakes hands exactly once with every other person. How many handshakes occur?
  • A576576
  • B276276
  • C552552
  • D2424
Show answer and explanation

Answer: B

Each pair shakes once: 24(241)2=5522=276\frac{24(24 - 1)}{2} = \frac{552}{2} = 276.

Question 2

At a meeting, each of 77 people shakes hands exactly once with every other person. How many handshakes occur?
  • A2121
  • B77
  • C4949
  • D4242
Show answer and explanation

Answer: A

Each pair shakes once: 7(71)2=422=21\frac{7(7 - 1)}{2} = \frac{42}{2} = 21.

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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