The local elementary school PTA is forming a 5 member committee to organize the campus beautification activities. Of the parents available to be chosen for the committee, 10 have children in kindergarten, 20 have children in 1st grade, 5 have children in 2nd grade, 15 in 3rd grade, 10 in 4th grade and 15 have children in 5th grade. No parent has children in more than one grade. How many ways can the committee be formed if 4th grade can have no more than 2 representatives?
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.
The local elementary school PTA is forming a 5 member committee to organize the campus beautification activities. Of the parents available to be chosen for the committee, 10 have children in kindergarten, 20 have children in 1st grade, 5 have children in 2nd grade, 15 in 3rd grade, 10 in 4th grade and 15 have children in 5th grade. No parent has children in more than one grade. How many ways can the committee be formed if 4th grade can have no more than 2 representatives?
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