The answer is 27/4 or 6 3/4
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
