Your local grocery store just received a large shipment of apples, oranges, pears, and bananas—more than $100$ pieces each. You are shopping at the store and will purchase your fruit for the week.
$1$. How many ways can you select $10$ pieces of fruit from your store’s supply of apples, oranges, pears, and bananas?
Is it like there are more than $400$ fruits in total, so is it $$\binom{400+10-1}{10-1}$$
$2$. How many ways can you select $10$ pieces of fruit from your store’s supply of apples, oranges, pears, and bananas if you need at least one piece of each kind of fruit?