Question

There are 5 hotels in Stony Brook. If 3 people check into hotels on September 12, what is the probability that they each check into a different hotel? (What assumptions are you making?) Make sure to define any notation you use to describe elements of the sample space

Answer 1

Answer:

0.48

Step-by-step explanation:

Our given parameters include:

There are 5 hotels in Stony Brook( i.e Number of hotels ) = 5

If 3 people check into hotels (i.e number of people that check-in) =3

This typical implies that each individual personnel out of 3 check-in 5 different hotels, therefore, the total outcomes = 5 × 5 × 5

= 125

Let's take an instance on the three personnel:

Let's say the first personnel check-in at one hotel out of the five hotels;

we have:

= 5C₁

= 5

And, the second personnel check-in at one hotel out of the four hotels; we have:

= 4C₁

= 4

Likewise the third personnel check-in at one hotel out of the three hotels; we have:

=3C₁

=3

∴ The probability that they each check-in into a different hotel can now be determined as:

= $\frac{5*4*3}{125}$

= 0.48