Question

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

Answer 1

This question is incomplete! here is the complete question with answer!

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

Step-by-step 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=(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=(5!)/(0!(5-0)!)=(5!)/(0!*5!)=1`

If car X has 1 feature included then:

`5C1=(5!)/(1!(5-1)!)=(5!)/(1!*4!)=5`

If car X has 2 features included then:

`5C2=(5!)/(2!(5-2)!)=(5!)/(2!*3!)=10`

If car X has 3 features included then:

`5C3=(5!)/(3!(5-3)!)=(5!)/(3!*2!)=10`

If car X has 4 features included then:

`5C4=(5!)/(4!(5-4)!)=(5!)/(4!*1!)=5`

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

`5C5=(5!)/(5!(5-5)!)=(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