GRE Math Challenge Question #18:
Any buyer of a new sports car has to pick between 2 of 5 options for seat colors and 3 of 4 options for dashboard accessories. How many different combinations of colors and dashboard options are available to this buyer?
A) 5
B) 6
C) 20
D) 40
E) 396
Solution with Explanation:
We know that this is either a combination or permutation. Since the order does not matter, we know that if we used the permutations formula we would be double counting some arrangements.
So the combination formula is n!/(r!(n-r)!), where r objects are chosen from a set of n objects.
In this case we have two types that we need to solve for and then multiply out to get our total options available.
Colors: 5!/(2!(5-2)!) = (5*4*3*2*1)/((2*1)(3*2*1)) => we can cancel out many numbers here; we are left with =>
(5*4)/(2*1) = 10 color choices.
Dashboard: 4!/(3!(4-3)!) => (4*3*2*1)/((3*2*1)(1)) => cancel out again and get 4 Dashboard choices.
Now we have to multiply these out to get the total choices available.
10*4 = 40 options
Correct Choice: D
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