# 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?

There are 40 different combinations of colors and dashboard options available to this buyer.

Combination is a counting technique where the order of the selected items from a collection does not matter. The formula in finding the number of combinations when ‘r’ items are chosen out of a total of ‘n’ objects.

nCr = n! / [r! (n - r)!]

If there are 2 of 5 options for seat colors, then using the formula, the number of combinations for the seat color is:

5C2 = 5! / [2! (5 - 2)!]

5C2 = 120 / 12

5C2 = 10

If there are 3 of 4 options for dashboard accessories, then using the formula, the number of combinations for the dashboard accessories is:

4C3 = 4! / [3! (4 - 3)!]

4C3 = 24 / 6

4C3 = 4

Multiplying the two results will give the total number of different combinations of colors and dashboard options available.

combination =  10 x 4

combination = 40

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