Ax1- probability with combinatorics

considering a sequence of ten coin flips: the number of possible outcomes is $2^{10}$

considering five cards dealt from a deck:

• for the first card, there are 52 possibilities, and for every other card, there is one fewer
• so the number of possible card sequences $=52\times 52\times 50\times 49\times 48=52!/47!$

for both these cases, order matters

the first case is called with replacement, the second is called without replacement

for the cards, generalising to $n$ choices and $r$ samples: