Question

You have 3 mammals and 3 reptiles in the zoo. You must feed each of them. You can select from the following foods to feed: banana, grapes, meat, oranges, lettuce, carrot, salmon, corn, apples.

(a) How many different ways can you feed each animal?

(b) How many different ways can you feed each animal if all the foods are different?

(c) How many different ways can you feed each animal if at least one mammal gets a banana and at least one reptile gets meat?

(d) How many different ways can you feed each animal if the oldest mammal gets the same food as the oldest reptile?

(e)How many different ways can you feed each animal if four of them is fed the same food and the other two are fed different food that is also different from the other four?

(f) You recently visited the market, and there is a deal where you can buy three different foods and get the same three for free. How many ways can you feed the animals under this deal?

Answer 1

a) There are nine types of food for every kind of animal, and there is a total of 6 animals. Thus the total number of ways is 6⁹.

b) If all the foods are different, then the first animal has nine choices, 2nd has 8 options, and so on. Thus the number of ways in which we can feed each animal different food is 9*8*7*6*5*4

c) First, we will give one mammal a banana and one reptile meat. It can be done in 3*3 = 9 ways. Now the remaining animals don't have any restrictions; thus, the total number of ways is 9*4⁹.

d) Let the oldest reptile gets one of 9 foods; then, the oldest animal also receives the same. It can be in 9 ways. Now the remaining animals don't have any restrictions; thus, the total number of ways is 9*4⁹.

e) Let 4 of them are given the same food, which has nine choices, and the remaining 2 gets a different food, which has eight options. Thus, the total number of ways is