spping around

You are given three spinning tops with six, eight and ten numbered sides respectively. In how many ways can the three tops fall if at least two of the tops fall on the side marked with the number '1'?




click on the title for the solution....




SOLUTION: 

To ensure you don't double count, consider the case where all three tops land on the number '1' separately. Thus, there are 5 possible arrangements when the eight-sided and ten-sided tops fall on '1', 7 arrangements when the six-sided and ten-sided tops fall on '1', and 9 arrangements when the remaining pair fall on '1'. We now add the additional case where all three tops land on '1', giving 5+7+9+1=22 possible outcomes.