# 19.2 Permutations and Probability

Permutations and probability are two closely related concepts in mathematics. Permutations are the number of ways a set of objects can be arranged in a certain order. Probability, on the other hand, is the likelihood that a certain event will occur. A deep understanding of these two concepts can help students gain a better understanding of the mathematics behind the world around them.

To better understand permutations and probability, it is important to look at an example. Let’s say you have a set of three cards: a King, a Queen, and a Jack. If you want to determine the different ways these three cards can be arranged, you would be looking at the number of permutations. In this case, there are six possible permutations: KQJ, KJQ, QKJ, QJK, JKQ, and JQK.

When it comes to probability, we can use the same example of the three cards. If you want to know the probability of drawing a King from a deck of cards, you would need to consider the number of Kings in a standard deck. There are four Kings in a standard deck of 52 cards, so the probability of drawing one is 4/52, or 1/13.

In addition to permutations and probability, the concept of combinations is also closely related to the two. Combinations are the different ways a set of objects can be grouped together without regard to order. For example, when looking at a set of three cards, there are three possible combinations: KQ, KJ, and QJ. The number of combinations is always smaller than the number of permutations.

To summarize, permutations and probability are two closely related concepts in mathematics. Permutations are the number of ways a set of objects can be arranged in a certain order. Probability is the likelihood that a certain event will occur. Combinations are the different ways a set of objects can be grouped together without regard to order. Understanding these concepts can help students gain a better understanding of the mathematics behind the world around them.

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In conclusion, 19.2 permutations and probability are two closely related concepts in mathematics. Permutations are the number of ways a set of objects can be arranged in a certain order while probability is the likelihood that a certain event will occur. Understanding these concepts can help students gain a better understanding of the mathematics behind the world around them.