Assume that you have laid out the namecards for 14 people, and you want to hide 4 golden tickets, at most one under each namecard. The total number of ways = 784
From the question, we have
The total number of people in each party = 8
The total number of winners in each party = 2
The total number of ways of selecting two winners from 8 people = P(8,2) = 28
The total number of ways of selecting two winners from each political party = 28*28 = 784
The total number of ways = 784
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly.
The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
Complete question:
In celebration of Chinese new year, you are arranging name cards for 16 people to sit around this table. Since the cards are placed on the rotating lazy Susan, the specific chair of a guest does not matter, only who is to their left and right. That is, two namecard arrangements are considered different iff there is a guest whose person on their right or left changes. Now when you hide four golden tickets under the placed name cards, you want to ensure that each party has two winners. In how many ways can you choose to do so?
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