Therefore there are 4 x 3 = 12 possibilities.
For each of these 4 first choices there are 3 second choices. The first choice can be any of the four colors. How many ways are there of picking up two pieces? Table 2 lists all the possibilities. Suppose that there were four pieces of candy (red, yellow, green, and brown) and you were only going to pick up exactly two pieces. Then, for each of these 18 possibilities there are 4 possible desserts yielding 18 x 4 = 72 total possibilities. Then, for each of these choices there is a choice among 6 entrées resulting in 3 x 6 = 18 possibilities. You can think of it as first there is a choice among 3 soups. How many possible meals are there? The answer is calculated by multiplying the numbers to get 3 x 6 x 4 = 72. Imagine a small restaurant whose menu has 3 soups, 6 entrées, and 4 desserts.
This means that if there were 5 pieces of candy to be picked up, they could be picked up in any of 5! = 120 orders. Where n is the number of pieces to be picked up. The formula for the number of orders is shown below. This makes six possible orders in which the pieces can be picked up. Similarly, there are two orders in which yellow is first and two orders in which green is first. There are two orders in which red is first: red, yellow, green and red, green, yellow. The question is: In how many different orders can you pick up the pieces? Table 1 lists all the possible orders. You are going to pick up these three pieces one at a time. Suppose you had a plate with three pieces of candy on it: one green, one yellow, and one red. The topics covered are: (1) counting the number of possible orders, (2) counting using the multiplication rule, (3) counting the number of permutations, and (4) counting the number of combinations. This section covers basic formulas for determining the number of various possible types of outcomes. Apply formulas for permutations and combinations.Calculate the probability of two independent events occurring.
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