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Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control.
Quantity A : Number of different combinations possible
Quantity B : 25
A The quantity in Column A is greater
B The quantity in Column B is greater
C The two quantities are equal.
D The relationship cannot be determined from the information given.
Answer:
A The quantity in Column A is greater
Explanation:
Lets first analyze the number of different combinations possible!
To find out the combinations we use the following formula:
The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter.
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Car X can have these 5 features: sunroof, stereo, tinted windows, leather seats and cruise control.
Car X has 2 options for each feature: Included or Not included
If car X has no feature at all then:
[tex]5C0=\frac{5!}{0!(5-0)!}=\frac{5!}{0!*5!}=1[/tex]
If car X has 1 feature included then:
[tex]5C1=\frac{5!}{1!(5-1)!}=\frac{5!}{1!*4!}=5[/tex]
If car X has 2 features included then:
[tex]5C2=\frac{5!}{2!(5-2)!}=\frac{5!}{2!*3!}=10[/tex]
If car X has 3 features included then:
[tex]5C3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!*2!}=10[/tex]
If car X has 4 features included then:
[tex]5C4=\frac{5!}{4!(5-4)!}=\frac{5!}{4!*1!}=5[/tex]
If car X has all of the 5 features included then:
[tex]5C5=\frac{5!}{5!(5-5)!}=\frac{5!}{5!*0!}=1[/tex]
Now sum all the possible combinations: 1+5+10+10+5+1=32
So, quantity A is 32 and quantity B is 25
Therefore, we can conclude that the quantity in column A is greater
