SOLUTION: How many ways can two cars and four trucks be selected from five cars and seven trucks to be tested for a safety inspection?

Algebra.Com
Question 1201863: How many ways can two cars and four trucks be selected from five cars and seven trucks to be tested for a safety inspection?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 350

Explanation:

The order of cars and trucks doesn't matter.
Use the nCr combination formula.

n = 5 cars total
r = 2 cars to pick
n C r = (n!)/(r!(n-r)!)
5 C 2 = (5!)/(2!*(5-2)!)
5 C 2 = (5!)/(2!*3!)
5 C 2 = (5*4*3!)/(2!*3!)
5 C 2 = (5*4)/(2!)
5 C 2 = (5*4)/(2*1)
5 C 2 = 20/2
5 C 2 = 10
There are 10 ways to pick two cars from a candidate pool of five cars total.

The value 10 can be found in Pascal's Triangle.
Look at the row that starts with 1,5,...
We're looking at the third slot because r starts at r = 0
r = 0 ... 1st slot
r = 1 ... 2nd slot
r = 2 ... 3rd slot

Repeat the previous set of steps to determine that 7C4 = 35, which is the number of ways to pick the four trucks from a pool of seven trucks.
The value 35 can be found in Pascal's Triangle in the row that starts with 1,7...
Look in the fifth slot (r = 4 --> 4+1 = 5th slot)

To recap we found that there are...The order doesn't matter.

In total there are 10*35 = 350 ways to pick two cars and four trucks from a pool of five cars and seven trucks. The order doesn't matter.

nCr calculator
https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
Pascal's Triangle
https://www.mathsisfun.com/pascals-triangle.html
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

By repeating the words from the problem's description, the number of different ways is

 = 10  multiplied by   = 35,  i.e.  

    . = 10*35 = 350.    ANSWER

Solved.

----------------------

This problem is on Combinations and on the Fundamental counting principle.

On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

On Fundamental counting principle,  see the lesson
    - Fundamental counting principle problems
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



RELATED QUESTIONS

How many ways can 4 cars and 3 trucks be selected from 8 cars and 11 trucks to be tested... (answered by madamecandy69)
How many ways can 3 cars and 4 trucks be selected from 6 cars and 11 trucks to be tested (answered by Boreal)
How many ways can 4 cars and 2 trucks be selected from 10 cars and 7 trucks to be tested... (answered by ikleyn)
How many ways can 2 cars and 3 trucks be selected from 7 cars and 9 trucks to be tested... (answered by ikleyn)
How many ways can five cars and three trucks be selected from nine cars and five trucks? (answered by stanbon)
A company has 8 cars and 11 trucks. The state inspector will select 3 cars and 4 trucks... (answered by ikleyn)
A tunnel toll is $1.25 for cars and $2.00 for trucks. In one hour $40.00 is collected... (answered by richwmiller)
A company owns a fleet of trucks and cars. The ratio of trucks to cars is 1:3 and there... (answered by solver91311)
A new car dealership sells cars and trucks at a ratio of 7 to 5. Last month the... (answered by LinnW)