Question

In a bag of 100 marbles comprised of many colors, 25 are blue. suppose marbles are selected at random.
a.in any set of 5 marbles, how many different ways could you arrange 3 bluemarbles?

Answer 1

Solution: The number of ways we can arrange 3 blue marbles if a set of 5 marbles is selected is:

$\binom{5}{3}=\frac{5!}{(5-3)!3!}$

                          $=\frac{120}{2 \times 6}$

                          $=\frac{120}{12}=10$

Therefore, there are 10 ways we could arrange 3 blue marbles.