Question

Coca-Cola comes in 2 low-calorie varieties: Diet Coke and Coke Zero. If a promoter has 10 cans of each how many ways can she select 3 cans of each for a taste test at the local mall?

Answer 1

There are 14,400 possible ways to do this

Explanation:

Here, we have a selection problem. What to use is combination obviously.

For a combination problem, we would be selecting a specific number from a given total. For a case where we have n number of things and we are looking for how many ways to select r number of things, this can be done in nCr ways and this is mathematically equal to n!/(n-r)!r!

For the Diet coke, she has 10 bottles and want to select 3 for tasting, the number of ways she can do this is mathematically equal to 10C3. Computationally this is equal to ;

10!/(10-3)!3! = 10!/7!3! = 120 ways

For the coke zero, we have the same pattern, selecting a total number of 3 out of 10. This means the same 10C3 with the answer being 120 ways also.

Now, the number of ways of selecting from both would be a multiplication of both answers which is 120 ways * 120 ways = 14,400 ways