Answer:
The number of ways to select 3 cars and 5 trucks is 69,06,900.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
It is provided that:
Number of different cars, n (C) = 25.
Number of different trucks, n (T) = 15.
Devin selects 8 vehicles to display on the shelf in his room.
Compute the number of ways in which he can select 3 cars from 25 different cars as follows:
[tex]{25\choose 3}=\frac{25!}{3!(25-3)!}=\frac{25\times24\times23\times22!}{3!\times22!}=2300[/tex]
There are 2300 ways to select 3 cars.
Compute the number of ways in which he can select 5 trucks from 25 different trucks as follows:
[tex]{15\choose 5}=\frac{15!}{5!(15-5)!}=\frac{15\times14\times13\times12\times 11\times10!}{5!\times10!}=3003[/tex]
There are 3003 ways to select 5 trucks.
Compute the total number of ways to select 3 cars and 5 trucks as follows:
n (3 cars and 5 trucks) = n (3 cars) × n (5 trucks)
[tex]={25\choose 3}\times {15\choose 5}\\=2300\times 3003\\=6906900[/tex]
Thus, the total number of ways to select 3 cars and 5 trucks is 69,06,900.
