Convert This to a Real Life Example

Let us try and convert this scary looking binomial to a simple real life situation.

What is $\dbinom{17}{a}$ ? It is the number of ways in which $a$ people can be chosen from a group of $17$ people. The same thing with the other two, $b,c$ . Now, this means that the given binomial expression is the number of ways in which we can choose $a+b+c=5$ people from $17+17+17=51$ people.

Hence, the answer is $\dbinom{51}{5}=2349060$ .