On a TV game show, a contestant is shown 8 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen ite

Question

On a TV game show, a contestant is shown 8 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen items need not be in any particular order. In how many ways can the contestant choose the three items?

Answer 1

We are going to need the Combination formula because in combinations the order doesn't matter.

 

n!/r!(n - r)!  where 'n' is the total number to choose from and 'r' is the number that needs to be chosen.

 

So, 'n' = 8 and 'r' = 3

 

Substitute the numbers into the formula and solve.

 

8!/(8 - 3)! = 40320/6(120) = 40320/720 = 56

 

 

Note: To solve factorials (!) by hand it would be:

 

8 * 7 * 6 * 5 * 4 * 3 * 2/3 * 2(5 * 4 * 3 * 2)