Question

It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 1616 students in the class, what is the probability that the first 22 presentations will be by Drake and Todd, in that order

Answer 1

`(1)/(240) = 0.0042` = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, since the order in which the students are chosen is important, the permutations formula is used to solve it.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

Desired outcomes:

Drake then Todd, so only one outcome, which means that
`D = 1`

Total outcomes:

Two students from a set of 16, so:

`T = P_(16,2) = (16!)/(14!) = 16*15 = 240`

What is the probability that the first 2 presentations will be by Drake and Todd, in that order?

`p = (D)/(T) = (1)/(240) = 0.0042`

`(1)/(240) = 0.0042` = 0.42% probability that the first 2 presentations will be by Drake and Todd, in that order.