Question

A company has 8 cars and 11 trucks.The state inspector will select 3 cars and 4 trucks to be tested for safety inspections in how many ways can this be done

Answer 1

Answer:

Number of ways to select 3 cars and 4 trucks = 18,480

Step-by-step explanation:

Let x be the number of ways to select 3 cars and 4 truck.

Given:

Total number of cars = 8

Total number of Trucks = 11

We need to find out how many ways can the inspector select 3 cars and 4 truck.

Solution:

Using combination formula.

$nCr = \frac{n!}{r!(n-r)!}$

Where, n = Total number of object.

m = Number of selected object.

We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.

So, we write the the combination as given below.

$8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection$

$\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x$

$x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}$

Factorial 5 and 7 is cancelled.

$x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}$                     ($3! = 6\ and\ 4! = 24$)

$x = (8\times 7) \times (11\times 10\times 3)$                ($\frac{9\times 8}{24}=\frac{72}{24}=3$)

$x=56\times 330$

x = 18480

Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,