After rolling the first ball of a frame in a game of 10-pin bowling, how many different pin configurations can remain (assuming all configurations are physically possible)?
Source: NCTM Mathematics Teacher, September 2006
A pin configuration is made up of ten pins each of which can be up or down. The number of possible configurations equals .
Let represent the number of pins left standing after a roll. In how many ways can they be left standing?
way to leave zero pin (bowl a strike)
ways to leave a single pin
ways to leave two pins
way to leave all ten pins (gutter ball)
Total number of possible ways