How many possible combinations can pennies be distributed?

Question
In how many ways can 3 girls divide 10 pennies if each must end up with at least one penny?




Solution
First, let us determine whether the above problem is an example of a permutation or combination problem OR the combination of both.

Combination is the various ways that the 10 pennies can be distributed to the 3 girls given that each girl must end up with at least 1 penny.
Permutation, on the other hand, is defined as the possible arrangements of the pennies.

Now, for the above problem, it does NOT matter what penny goes to each girl - what matters is that each gets at least a penny. Hence, the problem is both a combination and a permutation problem.

Second, the easiest way to solve a combination and permutation problem is by using the nPr function of your calculator.

• Turn on your calculator
• Key in '10' for the total number of pennies
  
• Press nPr
• Key in '3' for the total number of ways
• Press equal or enter key
• You get 720 possible combinations!
  

Please do not forget to leave a feedback in Allexperts.com AND a comment in this blog.