EXAMPLE 45 Number of permutations of nondistinct items

Brandon brings a healthy snack to school each day, consisting of 5 carrot sticks, 4 celery sticks, and 2 cherry tomatoes. If Brandon eats one item at a time, in how many different ways can he eat his snack?

Solution

We are seeking the number of permutations of items, of which are carrot sticks, are celery sticks, and are cherry tomatoes. Using the formula for the number of permutations of nondistinct items,

There are 6930 distinct ways in which Brandon can eat his snack.