Overview
Questions: The Google company must appoint three corporate officers: Chief Executive Officer (CEO), Executive Chairperson, and Chief Operating Officer (COO). The company also must appoint a Planning Committee with three different members. There are eight qualified candidates, and officers can also serve on the Planning Committee.
Question #1)
How many different ways can the officers be appointed? Show your work, and explain your solution.
Question #2)
Does order matter in question #1? Why or why not? Explain your answer.
Question #3)
How many different ways can the committee be appointed? Show your work, and explain your solution.
Question #4)
Does order matter in question #3? Why or why not? Explain your answer.
Background information you need to know: ( Please remember this is a foundational concept for this chapter. Please read the entire chapter of your textbook and watch all the videos related to this chapter to fully understand it.)
Permutation
Permutations of items are arrangements in which different sequences of the same items are counted separately.
For example, the letter arrangements of ABC, ACB, BAC, BCA, CAB, and CBA are all counted separately as six different permutations.
When n different items are available and r of them are selected without replacement (order matters in permutation) the number of different permutations is given by the formula below:
[Image unavailable: _{n} P_{r}=\frac{n !}{(n-r) !}]
| [Image unavailable: _{n} P_{r}] | = | permutation |
| [Image unavailable: n] | = | total number of objects |
| [Image unavailable: r] | = | number of objects selected |
Combination:
When n different items are available but only r of them are selected without replacement, the number of different combinations (order does not matter) is found by the formula:
[Image unavailable: _n C_r=\frac{n !}{r ! (n-r) !}]
| [Image unavailable: _n C_r] | = | number of combinations |
| [Image unavailable: n] | = | total number of objects in the set |
| [Image unavailable: r] | = | number of choosing objects from the set |
Example: "My fruit salad is a combination of apples, strawberry, blueberry, and bananas" We don't care what order the fruits are in, they could also be "strawberry, bananas, blueberry, grapes, and apples" or "blueberry, grapes, apples, bananas, and strawberry", it's the same fruit salad.