In Example 1.46, what 7-bit sequence corresponds to two apples and three carrots? What sequence corresponds to two apples and three bananas? What sequence corresponds to five apples?

Example 1.46.

An automated snack machine dispenses apples, bananas, and carrots. For a fixed price, the customer gets five items from among the three possible choices. For example, a customer could choose one apple, two bananas, and two carrots. To record the customer’s choices electronically, 7-bit sequences are used. For example, the sequence (0,1,0,0,1,0,0) means one apple, two bananas, and two carrots. The first group of zeros tells how many apples, the second group of zeros tells how many bananas, and the third group of zeros tells how many carrots. The ones are used to separate the groups of zeros. As another example, (0,0,0,1,0,1,0) means three apples, one banana, and one carrot. How many customer choices are there?