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?
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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):
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...
10 ways to pick the two cars from a pool of five cars.
35 ways to pick the four trucks from a pool of seven trucks.
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.
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