# Real examples of multinomial distribution

I found multinomial distribution really powerful in theory. But I don't know if my real case can be treated as multinomial. There are two cases:

1. There are $n$ students, $30\%$ chose apple, $40\%$ chose banana, $30\%$ chose grape. Then can I say the choice of single student follow a $\mathrm{Multinomial}(n,0.3,0.4,0.3)$ distribution?
2. Similar, say I have $n$ books, $30\%$ will be distributed to group 1, $40\%$to group 2, the rest to group 3. Then can I assume the allocation of a single book follows a multinomial distribution? What if I was to allocate money instead of books? In this case, money is continuous not discrete.
• Take care in interpretation. It's conceivable, for example, that the "choice of [any] single student" is not at all random and should not be described by a multinomial distribution. (Some students might hate bananas, for instance.) What a distribution can describe is a process for selecting the $n$ students from a population. For the multinomial distribution to apply, that process has to be analogous to picking slips of paper--one per student--out of a well-mixed bowl of a great many such slips.
– whuber
Jan 8, 2013 at 16:21
• youtube.com/watch?v=PxVnYVScU-o Jan 8, 2013 at 16:25