Question

Devin has a collection of 40 model vehicles which consists of 25 different cars and 15 different trucks. He selects 8 to display on the shelf in his room. How many different ways can he select 3 cars and 5 trucks?

Answer 1

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:

${n\choose k}=\frac{n!}{k!(n-k)!}$

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:

${25\choose 3}=\frac{25!}{3!(25-3)!}=\frac{25\times24\times23\times22!}{3!\times22!}=2300$

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:

${15\choose 5}=\frac{15!}{5!(15-5)!}=\frac{15\times14\times13\times12\times 11\times10!}{5!\times10!}=3003$

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)

                                     $={25\choose 3}\times {15\choose 5}\\=2300\times 3003\\=6906900$

Thus, the total number of ways to select 3 cars and 5 trucks is 69,06,900.