A school head wants to randomly choose 5 people from the staff of 30 to help out at the open day BBQ. In how many ways can this be done?

This is a combination problem, as the order in which the 5 people are chosen does not matter.

The formula for combinations is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of people (30 in this case) and r is the number of people to be chosen (5 in this case).

Plugging in the values, we get:

C(30, 5) = 30! / (5! * (30-5)!)
C(30, 5) = 142506

Therefore, there are 142506 ways in which the school head can randomly choose 5 people from the staff of 30 to help out at the open day BBQ.

The number of ways to choose 5 people from a staff of 30 is given by the combination formula:

C(n, r) = n! / (n-r)! / r!

where n is the total number of items and r is the number of items to be chosen.

In this case, n = 30 and r = 5, so the number of ways to choose 5 people from a staff of 30 is:

C(30, 5) = 30! / (30-5)! / 5! = 30! / 25! / 5! = 142,506

Therefore, there are 142,506 ways to choose 5 people from a staff of 30 to help out at the open day BBQ.