(a) Use the multiplicative principle to explain why the number of ways we can select five numbers from {1,2, ...,12} without replacement, where we care about the order of the selection, is equal to 12! 7! (b) Use the multiplicative principle to find the number of ways we can distribute 10 distinguishable ping-pong balls into 4 boxes. Explain your reasoning. You do not need to explicitly evaluate the number. (c) Write down an expression for the number of ways we can distribute 10 distinguish- able ping-pong balls into 4 boxes, where we require that every box contains at least one ball. You do not need to evaluate the expression or explain your answer.

A small hula-hoop was rolled on the ground.  After rolling exactly 6 times, it went 37.7 feet.     What is the Diameter of the hula-hoop?   You got an extra large hula-hoop that has a diameter twice the length of the small hula-hoop.     How far would it go if you got it to roll exactly 8 times?   show work