Using permutations, the 20 number different ways can the two positions be filled if each position can only be filled by one person.
According to the question,
Five people are applying for the positions of president and treasurer.
A permutations is an arrangement in a definite order of a number of objects taken some or all at a time.
[tex]P(n,r)=nP_{r} = \frac{n!}{(n-r)!}[/tex]
In order to find the number different ways can the two positions be filled if each position can only be filled by one person we can find using permutations
[tex]5P_{2} = \frac{5!}{(5-2)!}[/tex]
= [tex]\frac{120}{3*2}[/tex]
=20
Hence, using permutations, the 20 number different ways can the two positions be filled if each position can only be filled by one person.
Learn more about permutations here
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