Question

Suppose x coins are tossed. Write an expression to represent the number of possible outcomes.

Answer 1

two possible outcomes H or T for each toss,
counting principle tells you if you do this \(x\) times there are
\[2\times 2\times 2\times ...\times 2=2^x\] outcomes

Answer 2

If 1 coin is tossed there would be 2 possible outcomes, (Head or Tail).
Notice that the number of ways is 2 or 21.

If 2 coins are tossed there are 2 possible outcomes for the 1st coin.
Then for each of those 2 possible outcomes for the 1st coin, there are
2 possible otcomes for the 2nd coin. That's 2·2 or 4 ways. Notice that
the number of ways for 2 coins is 2·2 or 22.

If 3 coins are tossed there are 2 possible outcomes for the 1st coin.
Then for each of those 2 possible outcomes for the 1st coin, there are
2 possible otcomes for the 2nd coin. That's 2·2 or 4 ways for the first
two coins. Then for each of those 4 possible outcomes for the 1st coin,
there are 2 possible otcomes for the 3rd coin. That's 2·2·2 or 4·2 or
8 ways for the three coins. Notice that the number of ways for 3 coins
is 2·2·2 or 23.

Since
1. The number of ways for 1 coin is 21 and
2. The number of ways for 2 coins is 22 and
3. The number of ways for 3 coins is 23.
4.
...

So we can generalize and say:

x. The number of ways for x coins is 2x.

Answer 3

what @elyise said 'cept he\she means \(2^x\) not \(2x\)

Answer 4

im a he and yes i mean \[2^{x}\]