Worksheet: Finding Probability Using Permutations

Q1:

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

A
B
C
D
E

Q2:

A student ID number consists of 7 digits where each digit is a number from 0 to 9. Given that no digit can be repeated, find the probability that a randomly generated ID number is 7651932.

A0
B
C
D
E

Q3:

Two people are chosen randomly from a group of six hundred two. What is the probability that Adam was selected first and Lawrence second?

A0.5
B0
C
D
E

Q4:

Peter and Marilyn 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 Peter’s number will be 1 and Marilyn’s will be 2?

A
B
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E

Q5:

A company randomly assigns work identification numbers to their employees. Each number consists of 3 digits from 1–9. If the digits cannot be repeated, find the probability for a randomly generated number to be 315.

A
B
C
D
E

Q6:

Eleven members of a marching band, two girls and nine boys, always line in a row when they march. What is the probability that a girl will be at each end of the row if they line up in random order?

A0
B
C
D
E

Q7:

Gabriel is randomly arranging desks in circles for group activities. If there are 9 desks in his circle, what is the probability that Gabriel’s desk will be closest to the door?

A
B
C
D
E

Q8:

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

A
B0
C
D
E

Q9:

Lawrence, Douglas, 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 Douglas arriving first and Lawrence arriving second.

A
B
C
D
E

Q10:

Matthew 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.

A
B
C
D

Q11:

A number is formed at random using 2 distinct digits from the set . What is the probability that both the digits are odd?

A0
B
C
D
E

Q12:

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”.

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B
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D
E

Q13:

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”.

A
B
C
D
E

Q14:

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

A
B
C
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E

Q15:

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

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B
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E

Q16:

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

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B
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D
E

Q17:

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

A
B
C
D
E