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Three-Digit Permutation Probability Word Problem
Published on August 15, 2026
Statistics
Calculate the probability of forming a three-digit number beginning with a specific digit using the numbers 7, 8, and 3 without repetition. The total number of outcomes is 6, and the favorable outcomes are 2, resulting in a probability of 1/3.
Question
Answer
To solve the math problems presented in the image, let’s go through them one by one.
Problem 2
Question: “I write down a three-digit number using each of the digits 7, 8 and 3 once only. What is the probability that the number I write begins with the digit 3?”
Step-by-step solution:
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Identify the total number of possible outcomes:
We are forming a three-digit number using the digitswithout repetition. The total number of ways to arrange these three distinct digits is given by the number of permutations of 3 items, which is (3 factorial). The possible numbers are:. -
Identify the number of favorable outcomes:
We want to find how many of these numbers begin with the digit. If the first digit is fixed as , we only need to arrange the remaining two digits ( and ) in the remaining two positions. The favorable numbers are:and . -
Calculate the probability:
The probabilityis the ratio of the number of favorable outcomes to the total number of outcomes. Simplifying the fraction:
Answer for Problem 2: The correct option is
Problem 3
Question: “How many eighths are there in 7?”
Step-by-step solution:
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Understand the question:
An “eighth” is the fraction. The question asks how many times fits into the whole number . This is equivalent to solving for in the equation: -
Perform the calculation:
To find, multiply both sides by :
Alternatively, you can think of it this way: there are
Answer for Problem 3: There are