Answer: D. 1816214400
Step-by-step explanation:
When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : Total player = 15
Required number of players for Batting order = 9
Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]
[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]
[tex]=1816214400[/tex]
∴ The number of different ways can he arrange the players in the lineup = 1816214400
Hence, the correct answer is D. 1816214400
