Suppose that a company will select 3 people from a collection of 15 applicants to serve as a regional manager, a branch manager, and an assistant to the branch manager. In how many ways can the selection be made? Explain how you got your answer.

Answer: 2730Step-by-step explanation:Given : The number of applicants  =15 The number of posts for which candidates have been applied = 3To find the number of selections we use permutations since here order matters.The permutations of n things taking m at a time is given by :-[tex]^nP_m=\dfrac{n!}{(n-m)!}[/tex]Then , the required number of ways is given by [Put n = 15 and m = 3] :-[tex]^{15}P_3=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15\times14\times13\times12!}{12!}\\\\15\times14\times13=2730[/tex]Hence, the number of ways the selection can be made = 2730