In a group of 65 students there are 30 math majors and 35 computing science majors. In how many ways can a committee of 6 students be selected if: (a) there are no restrictions (b) there must be 5 math majors and 1 computing science major (c) there must be more computing science majors than math majors (d) there is a chair that must be a math major, a vice-chair that must be a computing science major and then 4 other committee members. (Type your answers below. You do not have to calculate the actual number. e.g. 34 * C(8,3) would be fine.)
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.
Discrete Math :
In a group of 65 students there are 30 math majors and 35 computing science majors. In how many ways can a committee of 6 students be selected if:
(a) there are no restrictions
(b) there must be 5 math majors and 1 computing science major
(c) there must be more computing science majors than math majors
(d) there is a chair that must be a math major, a vice-chair that must be a computing science major and then 4 other committee members.
(Type your answers below. You do not have to calculate the actual number. e.g. 34 * C(8,3) would be fine.)
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