A computer programming team has 15 members. Seven members are senior and eight members are junior programmers. Answer each of the following questions and enter an exact numerical value (that is, an integer) in the box. a) How many ways can a group of seven be chosen to work on a project? b) How many groups of seven can be chosen with at least three senior programmers? c) Suppose two members refuse to work together. How many groups of seven can be chosen to work on a project?
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.
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