Suppose that a college of engineering has seven departments, which we denote by a, b, c, d, e,f, and g. Each department has one representative on the college’s student council. From these seven representatives, one is to be chosen chair, another is to be selected vice-chair, and a third will be secretary. How many ways are there to select the three officers? Number of ways to select a chair, a vice chair and a secretary is computed as the number of permutation of 7 people taken 3 at a time which is computed as: = 7*6*5 = 210 Therefore there are 210 ways here. My question is why it is computed as = 7*6*5? Where does the 6 and 7 come from? Thanks.
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.
Suppose that a college of engineering has seven departments, which we denote by a, b, c, d, e,f, and g.
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Each department has one representative on the college’s student council. From these seven representatives, one is to be chosen chair, another is to be selected vice-chair, and a third will be secretary. How many ways are there to select the three officers?
Number of ways to select a chair, a vice chair and a secretary is computed as the number of permutation of 7 people taken 3 at a time which is computed as:
= 7*6*5
= 210
Therefore there are 210 ways here.
My question is why it is computed as = 7*6*5? Where does the 6 and 7 come from?
Thanks.
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