Chapter 9.1, Problem 50E

Solution

To state: The reason why $C_{{12}_2}=C_{{12}_{10}}$ if a fresh carton containing one dozen eggs and you need to choose two for breakfast.

The resultant answer is $C_{{12}_2}=C_{{12}_{10}}$ because both represent the same answer.

Given information:

A fresh carton contains one dozen eggs and you need to choose two for breakfast.

Explanation:

The given expression is: $C_{{12}_2}=C_{{12}_{10}}$

Total number of eggs in the carton is 12 and out of this 2 eggs are to be chosen. Then the expression for it will become: $C_{{12}_2}$

Now observe it that every time 2 eggs are chosen from the carton, at the same time you are also choosing that 10 eggs are not to be eaten. The expression for not choosing 10 eggs for eating will become: $C_{{12}_{10}}$

Therefore, it can be said that $C_{{12}_2}$ and are $C_{{12}_{10}}$ equal.