Introduction to Probability

Question

A teacher selects 3 students from a class of 24 to present their reports. Find the number of orders 3 students can be assigned to present.

number of orders=

Answer 1

The number of ways of choosing r items from a population of n, where order matters, is : _nP_r = n!/(n-r)!

₂₄P₃ = 24!/(24-3)! = 24*23*22 = 12144

Without using the permutation formula, we can reason this out: there are 24 choices for the first student selection, 23 for the 2nd, and 22 for the 3rd, giving you 24*23*22 different orderings, as we saw with the formula.

[ When order does not matter, then the selection is _nC_r = n!/ ((n-r)!r!). One example where you may see this: How many 5-card poker hands have exactly one pair? Because the order in which they are dealt does not matter, there is that extra division of r! to remove the overcounted combinations. ]