A company just hired 8 new secretaries to place in various departments, and the marketing department has 4 different secretarial positions that are currently open. In how many ways can those 4 positions be filled?
Question
A company just hired 8 new secretaries to place in various departments, and the marketing department has 4 different secretarial positions that are currently open. In how many ways can those 4 positions be filled?
Solution
This is a permutation problem because the order in which the secretaries are placed matters (i.e., Secretary A being placed in Position 1 and Secretary B in Position 2 is different from Secretary B being placed in Position 1 and Secretary A in Position 2).
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of options,
- r is the number of options to choose,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
In this case, n = 8 (the total number of new secretaries) and r = 4 (the number of open positions).
So, the calculation would be:
P(8, 4) = 8! / (8-4)!
= 87654321 / 4321
= 876*5
= 1680
So, there are 1680 different ways the 4 positions can be filled by the 8 new secretaries.
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