They are not hard to count.
|a-b|=c
a and b are interchangeable so there are really twice as many oucomes in the sample space
So that is 30 possible outcomes
Count those with a 3 and double it as well. 7*2=14 favourable outcomes
Prob is 14/30 = 7/15
a | b | c | |
6 | 5 | 1 | |
5 | 4 | 1 | |
3 | 4 | 3 | 1 |
3 | 3 | 2 | 1 |
2 | 1 | 1 | |
6 | 4 | 2 | |
3 | 5 | 3 | 2 |
4 | 2 | 2 | |
3 | 3 | 1 | 2 |
3 | 6 | 3 | 3 |
3 | 5 | 2 | 3 |
3 | 4 | 1 | 3 |
6 | 2 | 4 | |
5 | 1 | 4 | |
6 | 1 | 5 |
Modular arithmetic
https://web2.0calc.com/questions/number-theory_29
The American Mathematics College is holding its orientation for incoming freshmen. The incoming freshman class contains fewer than 500 people. When the freshmen are told to line up in columns of 23, 22 people are in the last column. When the freshmen are told to line up in columns of 21, 14 people are in the last column. How many people are in the incoming freshman class?
Chris, Alan and I have all answered this in different ways. For me, Alan's way is simple, different and interesting.