+0

# counting

0
74
1

How many 3-digit numbers contain exactly one 1 and exactly one 2? Examples include 512 and 271.

Jul 6, 2022

#1
+2448
-1

There are 8 choices for the remaining number (0, 3, 4, 5, 6, 7, 8, 9)

Once we select this number, there are $$3! = 6$$ numbers that can be made.

However, we need to subtract 2 because 0 can't be a leading digit.

This makes for $$8 \times 6 - 2 = \color{brown}\boxed{46}$$ numbers.

Jul 6, 2022

#1
+2448
-1

There are 8 choices for the remaining number (0, 3, 4, 5, 6, 7, 8, 9)

Once we select this number, there are $$3! = 6$$ numbers that can be made.

However, we need to subtract 2 because 0 can't be a leading digit.

This makes for $$8 \times 6 - 2 = \color{brown}\boxed{46}$$ numbers.

BuilderBoi Jul 6, 2022