Question

Nineteen vintage vehicles(12 cars and 7 trucks) have been brought by their owners to a car show.

In How many ways could the 6 vehicles be picked, if the decision has been made to have four cars and two trucks in the picture?

Answer 1

Solution:

Number of cars = 12

Number of trucks = 7

We have to select 6 vehicles such that it contains 4 cars and 2 trucks.

Number of ways of selecting k objects from n objects is given by,

Hence, number of ways of selecting 4 cars from 12 cars is,

Number of ways of selecting 2 trucks from 7 trucks is,

Using, multiplication law of permutation and combination, we get the total number of selecting 6 vehicles such that it contains 4 cars and 2 trucks. The total number of ways of picking is,

Hence, total number of ways by which 6 vehicles can be picked, if the decision has been made to have four cars and two trucks in the picture is 10395.