Question

Suppose "35" cars start at a car race. In how many ways can the top 3 cars finish the​ race?
The number of different top three finishes possible for this race of 35 cars is 39,270. (Use integers for any number in the expression.)

Answer 1

Answer:

The  value  is   $\left 35 } \atop }} \right. P_3 = 39270$

Step-by-step explanation:

From the question we are told that

    The  total number of cars is  $n = 35$

     The  number cars considered is  $r = 3$

Generally the number of different top three finishes possible for this race of 35 cars  is mathematically represented as

       $\left n } \atop }} \right. P_r = \frac{n!}{(n - r) !}$

       $\left 35 } \atop }} \right. P_3 = \frac{35! }{(35 - 3) !}$

       $\left 35 } \atop }} \right. P_3 = \frac{35 * 34 * 33 * 32! }{32 !}$

       $\left 35 } \atop }} \right. P_3 = 39270$