In one class 18 students play basketball, 14 students play soccer and 10 students play volleyball. 5 students play soccer and volleyball, 7 students play basketball and volleyball and 10 students play basketball and soccer. 4 students play all three sports. How many students are in the class if every student plays at least one sport?
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.
In one class 18 students play basketball, 14 students play soccer and 10 students play volleyball. 5 students play soccer and volleyball, 7 students play basketball and volleyball and 10 students play basketball and soccer. 4 students play all three sports. How many students are in the class if every student plays at least one sport?
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