Problem number six. Ria has three counters marked 1, 5, and 11 as shown. She wants to place them side by side to make a four-digit number. How many different four-digit numbers can she make? So first, we will imagine putting the counter 5 first. There are two different ways to do it. We do 5, 1, 11, or 5, 11, 1. But either way, we will only get one number, which is 5,111. If we imagine putting the counter 1 first, then we can do 1, 5, 11, or 1, 11, 5. And that will give us two new numbers, 1,511 and 1,115. Finally, if we put the counter with 11 first, we will get two possibilities, 11, 1, 5, or 11, 5, 1. The first of these is already a number that we got previously, 1,115, and so we shouldn't count it again. The second one is a new number, 1,151, and so we should count it. And so as you can see, there are four green numbers, which are the distinct numbers that we can form through this process. And that means that the answer is B, four.

four-digit numbers

counters

distinct combinations

number formation

Ria