An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 2020 students in the school. There are 1193 students in the Spanish class, 1236 in the French class, and 1134 in the German class. There are 660 students that are in both Spanish and French, 521 that are in both Spanish and German, and 572 that are in both French and German. In addition, there are 200 students taking all 3 classes. Ten students are selected at random. What is the probability that exactly four students are taking at least two language classes? You do not have to simplify.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
An elementary school is offering 3 language classes: one in Spanish, one in French,
and one in German. The classes are open to any of the 2020 students in the school. There are
1193 students in the Spanish class, 1236 in the French class, and 1134 in the German class.
There are 660 students that are in both Spanish and French, 521 that are in both Spanish and
German, and 572 that are in both French and German. In addition, there are 200 students
taking all 3 classes. Ten students are selected at random. What is the
four students are taking at least two language classes? You do not have to simplify.
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