Hands of five cards

Text

From a deck of $40$ Neapolitan cards, in how many ways can a “hand” of $5$ cards be dealt (order does not matter)?

Solution

We choose $5$ distinct cards from $40$ without regard to order: these are combinations, $N = \binom{40}{5} = \frac{40\cdot 39\cdot 38\cdot 37\cdot 36}{5!} = \frac{78\,960\,960}{120} = \boxed{658\,008}.$