Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

How many three-digit numbers are there that contain at least one of the digits 1, 2, or 3?  To begin, we can count the number of three-digit numbers without any of the digits 1, 2, 3, and then subtract them from the total number of three-digit numbers.  We know that there are 900 three-digit numbers from 100 to 999. In three-digit numbers without 1, 2, or 3, there are six options for the first digit,  seven for the second, and also seven for the third. Therefore, there are 294 three-digit numbers containing none of 1, 2, or 3.  Then we can find the complement and find that there are 606 three-digit numbers with at least one of the digits 1, 2, or 3.

Video Summary

The task is to determine how many three-digit numbers contain at least one of the digits 1, 2, or 3. There are 900 total three-digit numbers ranging from 100 to 999. To find those without any of the digits 1, 2, or 3, we examine the choices for each digit: 6 options for the first digit (4-9), and 7 options each for the second and third digits (0, 4-9), totaling 294 such numbers. Subtracting this from the total, 900 - 294, we find there are 606 three-digit numbers that include at least one of the digits 1, 2, or 3.

Keywords

three-digit numbers

digits 1 2 3

number calculation

digit exclusion

mathematical problem