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2. On the Internet, you find an Latin quiz with 10 matching vocabulary questions. Your 3 year old niece randomly matches the
words with the definitions. What is the probability that she makes 100 on the quiz?
Does the order matter? Yes -
This is a permutation
Will all of the words be matched? Yes -
Can we use factorials? Yes -
How many different ways can the answer key be arranged?
P(all correct)
(Enter your answer as a reduced fraction using/ for the fraction bar.)

Sagot :

Vipinmurlidharidn

Answer:

Assume that there is a Latin quiz with 10 matching vocabulary questions, and your niece try to match them randomly. Then, the probability that she gets the first item right is

1

10

since there is only one correct answer for this item out of 10 options. Now, the probability that she gets the second item right is

1

9

since there is only one correct option and there is only 9 options left to choose from. So, in a similar fashion, the probability that she will get the third item correct is

1

8

, the fourth item correct is

1

7

and so on. Therefore, the probability that she will match them all correctly (getting a 100 on the quiz) is equal to

1

10

⋅

1

9

⋯

1

2

⋅

1

1

=

1

10

!

=

1

3628800

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