There are 24 members on a swim team. how many different combinations of 5 swimmers can be chosen to sit in the front row for a team photo?

The number of combinations for picking a number of items from a given selection is found using this formula: nCr = n! / (n - r) ! r! where:

n = size of the selection

r = number of items being picked

In the case of the question, there is a selection of 24 people of which 5 will be chosen to sit in the front row so:

n = 24

r = 5

The number of combinations is 24C5 = 42504

Note: scientific calculators, e. g. Casio ones, have a button for the nCr formula.