Question

An administrative assistant has 4 blue filefolders, 3 red
folders, and 3 yellow folders on her desk. Each folder contains different
information, so two folders of the same color should be viewed as being
different. She puts the file folders randomly in a box to be taken to a
meeting. Find each probability.
A. P(4 blue, 3 red, 3 yellow, in that order)
B. P(first 2 blue, last 2 blue)

Answer 1

There are a total of 10! arrangements
A) There are 4! ways to arrange the blue, 3! for red, 3! for yellow
There is only 1 possible grouping since the blue must come first, then red, then yellow
\[P = \frac{4!3!3!}{10!}\]

Answer 2

B) same logic, there are 6 folder in between that can be arranged in any order
\[P = \frac{6!2!2!}{10!}\]