There are ten pins in ten pin bowling as that is the nature of that sport. In 5 pin bowling, there are 5 pins.
No tin pins, ten in ten pin
In tenpin bowling, there are ten pins per lane. In 9 pin there are nine. In 5 pin there are five.
In ten pin bowling, there are four pins on the back row.
In the pins, there are none. In the ball, there are 3.
4 hence 'ten pins' 4 at the back, then 3, then 2, then 1 at the front.
Bowling alley proprietors in Connecticut invented ten-pin bowling. In 1841, there was a lot of crime at the nine-pin bowling centers that were popular then, and to end the problem the Connecticut legislature banned "bowling at Nine Pins." The proprietors added a tenth pin to get around the ban. For some reason the legislature didn't go back and ban "bowling at Ten Pins."