Respuesta :
Answer:
D. 2730
Step-by-step explanation:
I just had this question on FLVS yesterday.
you use factorials for this:
15!/12!
15*14*13*12!/12!
15*14*13
2730
Number of ways in which 3 positions can be filled are 2730.
What is permutation and combinations?
The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.
If n things taken r at a time and n! = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1
⇒Permutation,
[tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]
Now it is given that number of candidates, n = 15
and number of position, r = 3
Hence number of ways positions can be filled-
[tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]
⇒ [tex]P(15,3) =\frac{15!}{12!}[/tex]
⇒ P(15,3) = (15 × 14 × 13)12!/12!
⇒ P(15,3) = (15 × 14 × 13)
⇒ P(15,3) = 2730
∴ Number of ways in which 3 positions can be filled are 2730.
More about Permutation :
https://brainly.com/question/27951291
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