Exercise #3 (Portfolio) Answer the following. 1. In how many ways can a committee of three be formed from a group of 10 members? 2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committee be formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committee consists of teachers only? 3. From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can this be done? 4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu?
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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