Question 1192079: A math club has 30 members. During their acquaintance gathering, they have to choose 3 officers: president, vice - president, and secretary. If each office is to be held by 1 person and no person can hold more than one office, how many ways can these offices be filled?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
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Start at 30 and count down by 1 until three slots are filled.
30 choices for president
29 choices for VP
28 choices for secretary
Then multiply out those items.
There are 30*29*28 = 24,360 different ways to fill these three positions. Order matters.
Order matters because ABC is different from BAC as shown below- ABC means person A is president, B is VP, C is secretary
- BAC means person B is president, A is VP, C is secretary
This is just one example.
Since order matters, you can use the nPr permutation formula with n = 30 and r = 3. This is an alternative pathway but the steps mentioned above are an easier route.
Answer by ikleyn(52778)  (Show Source):
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