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?

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:

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:

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:

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)

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

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step-by-step explanation:

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

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