1. A fast-food restaurant has a meal special: $5 for a drink, sandwich, side item and dessert. The choices are: a. Sandwich: Grilled chicken, All Beef Patty, Vegeburger and Fish Filet. b. Side: Regular fries, Cheese Fries, Potato Wedges. c. Dessert: Chocolate Chip Cookie or Apple Pie. d. Drink: Fanta, Dr. Pepper, Coke, Diet Coke and Sprite. How many combos are possible?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
1. A fast-food restaurant has a meal special: $5 for a drink, sandwich, side item and dessert. The choices are:
a. Sandwich: Grilled chicken, All Beef Patty, Vegeburger and Fish Filet.
b. Side: Regular fries, Cheese Fries, Potato Wedges.
c. Dessert: Chocolate Chip Cookie or Apple Pie.
d. Drink: Fanta, Dr. Pepper, Coke, Diet Coke and Sprite.
How many combos are possible?
2. You take a survey with five “yes” or “no” answers. How many different ways could you complete the survey?
3. A company puts a code on each different product they sell. The code is made up of 3 numbers and 2 letters. How many different codes are possible?
4. A student has to take one course of physics, one of science and one of mathematics. He may choose one of 3 physics courses (P1, P2, P3), one of 2 science courses (S1, S2) and one of 2 mathematics courses (M1, M2). In how many ways can this student select the 3 courses he has to take?
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