Lesson Worksheet: Probability with Permutations and Combinations Mathematics

In this worksheet, we will practice using permutations and combinations to calculate the probability of an event.


Hassan and Fawaz each bought one raffle ticket. If 50 tickets were randomly sold, what is the probability that Hassan got ticket number 20 and Fawaz got ticket number 26?

  • A12450
  • B1325
  • C25
  • D0
  • E150


Hassan, Faisal, and three of their coworkers each take the bus to work. If they each have an equal chance of arriving first, determine the probability of Faisal arriving first and Hassan arriving second.

  • A125
  • B15
  • C25
  • D115
  • E120


A small combination padlock can be opened by entering three different specified numbers from 1 to 9 in a specified order. Naser has 10 attempts to guess the combination. Determine the probability of him opening the lock.

  • A112
  • B172
  • C5252
  • D10729
  • E542


Naser received 10 letters in the mail. If he can read them in any order, determine the probability that he reads the letter from his parents and then that from his grandmother before the others.

  • A15
  • B190
  • C150
  • D1100


A number is formed at random using 2 distinct digits from the set {2,5,8,9}. What is the probability that both the digits are odd?

  • A0
  • B16
  • C14
  • D12
  • E34


The letters I, I, I, I, P, P, S, S, S, S, and M are placed in a bag. Determine the probability of randomly selecting letters from the bag in an order that spells the word “MISSISSIPPI”.

  • A1831600
  • B111
  • C169300
  • D311
  • E134650


The letters E, R, R, R, and O are placed in a bag. Determine the probability of randomly selecting letters from the bag in an order that spells the word “ERROR”.

  • A160
  • B16
  • C120
  • D15
  • E1120


Bandar and Abdulrahman are twins in a class of 17 students. 17 chairs are placed in a line for an assembly and the students are randomly assigned a seat. What is the probability of the twins sitting in the first two seats?

  • A2136
  • B18
  • C1136
  • D1272
  • E117


Fahd and Kayan are graduating in a class of 57 students. If each student is assigned a number from 1 to 57 at random, what is the probability that Fahd’s number will be 1 and Kayan’s will be 2?

  • A13249
  • B13192
  • C31913192
  • D257
  • E5557


If you randomly select a permutation of the letters shown, what is the probability that they spell KINETICS?

  • A120160
  • B128
  • C18
  • D156
  • E140320

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