3. 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?

A 3
B 4
C 6
D 8
E 9
Solution
B

The three counters can be arranged in six ways. However, when the counters with 1 and 11 on are placed side-by-side, the four-digit number formed will look the same whichever way round these two counters are placed. As these counters can be next to each other if they are both before the counter with five on or both after the counter with 5 on, this means only four different numbers can be made, namely $1115,1151,1511$ and 5111 .