Takumi's favorite clothing store is a large store with a large inventory. Many items are on sale, but the store has
a strange policy. You cannot find out if an item is on sale until you check out at the register. The store boasts
that 60% of the items in the store are on sale. Takumi is curious and calls the company headquarters. They
confirm that the items are all independently on sale.
a. As Takumi is checking out, what is the probability that the first item on sale is the third item checked out?
b. If he purchases 8 items of clothing, what is the probability that 5 of them will be on sale?
c. If Takumi plans to purchase a large number of items, what is the probability that he will have to wait longer
than 4 items before seeing the first item on sale?