Question

Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control.

Answer 1

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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.

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

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:

$5C0=\frac{5!}{0!(5-0)!}=\frac{5!}{0!*5!}=1$

If car X has 1 feature included then:

$5C1=\frac{5!}{1!(5-1)!}=\frac{5!}{1!*4!}=5$

If car X has 2 features included then:

$5C2=\frac{5!}{2!(5-2)!}=\frac{5!}{2!*3!}=10$

If car X has 3 features included then:

$5C3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!*2!}=10$

If car X has 4 features included then:

$5C4=\frac{5!}{4!(5-4)!}=\frac{5!}{4!*1!}=5$

If car X has all of the 5 features included then:

$5C5=\frac{5!}{5!(5-5)!}=\frac{5!}{5!*0!}=1$

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