Each coin can show either a head or a tail, giving 2 possibilities per coin. For 12 coins, the total number of arrangements is given by:

\(2^{12} = 4096\)

To find the number of arrangements with 7 heads and 5 tails, use the combination formula:

\(\binom{12}{7} = \frac{12!}{7!5!} = 792\)