coin flipping

Just the formula of 2^n for n number of coins.

When you flip a coin, there are only $2$ possible outcomes, a head $(\textrm{denote by } H)$ or a tail $(\textrm{denote by } T)$ . Thus, the sample space of possible outcomes for the $i^{\textrm{th}}$ coin, when flipped, is $S_i=S=\{H,T\} \implies n(S)=2$ .

When $33$ coins are flipped, each of the coins can give either one of the outcomes from $S$ and their outcomes are independent of the outcomes of the other coins. Using the rule of product, we have,

Total no. of outcomes $=\displaystyle \prod_{i=1}^{33} n(S) = 2^{33}=\boxed{8589934592}$

a simple solution for it could be 2^11 2^11 2^11 i.e = 2048 * 2048 * 2048

which is equal to = 8589934592

for one coin its 2^1=2 for 2 coins its 2^2 =4 so for 33 coins its 2^33=8589934592