Example problem:
A restaurant offers a special deal where customers can choose any 3 items from a menu of 10 items for a discounted price. How many different combinations of 3 items can a customer choose?
Solution:
To solve this problem, we can use the combination formula, which is given by:
nCr = n! / r!(n-r)!
Where n is the total number of items on the menu (10 in this case), r is the number of items to choose (3 in this case), and the exclamation mark denotes the factorial of a number.
Plugging in the values into the formula:
10C3 = 10! / 3!(10-3)!
10C3 = 10! / 3!7!
10C3 = (10 x 9 x 8 x 7!) / (3 x 2 x 1 x 7!)
10C3 = 120
Therefore, there are 120 different combinations of 3 items that a customer can choose from the menu.
Give an example problem where you would use Combination skills and formula to solve. Solve your example problem showing all your steps
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