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Chapter 9: Problem 41

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?

Short Answer

Expert verified
There are 11880 different ways the offices can be filled.

Step by step solution

01

Analyze the problem

This problem is about permutations - specific arrangements of items, where the order of selection matters. Here, we have 12 candidates and we are to fill 4 positions. A candidate cannot hold more than one position.
02

Calculate permutations

To calculate the number of ways, we can use the formula for permutations of a set: nPr = n! / (n - r)! Here n is the total number of candidates (12), and r is the number of positions to be filled (4). We use factorials (!) in the calculation, which are the product of all positive integers up to a given number.
03

Substitute and simplify

Now we can substitute our values into the formula. So, we have 12P4 = 12! / (12-4)! = 12! / 8! = 12 x 11 x 10 x 9 = 11880.

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