Question

Suppose a bag of colored marbles contains 15 marbles. If you draw one marble at a time from the bag, without replacement, how many different ways can you draw all of the marbles from the bag?Remember that "without replacement" means that the marbles are not returned to the bag after they are chosen.Write your answer in factorial notation.

Answer 1

The number of different ways to draw all 15 marbles from a bag without replacement is 15!, the factorial of 15.

Step-by-step explanation:

The question asks about the number of different ways you can draw all 15 marbles from a bag without replacement. This is a problem of permutations where the order in which marbles are drawn matters. To find the number of ways to draw all marbles, we simply calculate the factorial of the total number of marbles. The factorial notation for the number of ways to draw 15 marbles is 15!, which is the product of all positive integers up to 15.

Answer 2

We can solve the problem using the counting principle

Let:

N = Number of marbles

P = Number of ways you can draw all of the marbles

so:

`\begin{gathered} P=N\cdot(N-1)\cdot(N-2)... \\ so: \\ P=N! \\ P=15! \\ P\approx1.3*10^(12) \end{gathered}`

Answer:

1.3x10¹²