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Selecting Cards Cards numbered 1–10 are shuffled and dealt face down. What is the probability that they are in order?

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

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University of St. Thomas

Idaho State University

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Lectures

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01:21

Ten cards are numbered 1 t…

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In a deck of cards there a…

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00:59

01:19

Find the probability for t…

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Determine the probability.…

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Suppose that 3 cards are d…

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Find the probability of ea…

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An experiment consists of …

so suppose we have 10 cards numbered 1 to 10 and we shuffle them and face them down. And we want to know the probability of these cards in order. So the probability that they're in order equals the number of ways to sort them in order, divided by the total number of ways to sort them. And in this case, the number of ways, um to sort in order is simply one, because there is only one way to make them in order. Eso next, we're going to focus on the denominator and recall the definition of permutation. Um, if we want toe if we wanna select are objects out of n and sort these objects in order there are We want to know how many ways we could do that. And we use this notation. NPR and the Sequels and factorial divided by and minus are factorial so in our problem and equals r equals 10 because we want Thio select 10 cars out of 10 and short thes 10 cards, right, so 10 p 10 equals 10 factorial and divided by zero factorial and know that zero factorial equals one. So this simply goes to 10 factorial So finally we can compute. The probability of sorting these cards in order equals one divided by 10 factorial. And this is 10. Factorial is quite a large number. Mhm. We should use a calculator for this. Andi, this goes to 2.8 times turned to 97 which is a very small number.

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