How many outcomes are there for a tree diagram if you flip 3 coins, if each outcome counts only the number of heads.

When flipping 3 coins, each coin has 2 possible outcomes: heads (H) or tails (T).

1. For the first coin, you have 2 outcomes: H or T.
2. For the second coin, you also have 2 outcomes: H or T.
3. For the third coin, you again have 2 outcomes: H or T.

To find the total number of outcomes, you multiply the number of outcomes for each event. So, 2 (for the first coin) * 2 (for the second coin) * 2 (for the third coin) = 8 total outcomes.

However, the question asks for the number of outcomes counting only the number of heads. This means we are interested in the combinations of heads that can occur, not the specific order in which they occur.

1. No heads: This can only happen in one way, which is when all three coins land tails (TTT). So, there is 1 outcome with no heads.

2. One head: This can happen in three ways, which are when one coin lands heads and the other two land tails (HTT, THT, TTH). So, there are 3 outcomes with one head.

3. Two heads: This can also happen in three ways, which are when two coins land heads and one lands tails (HHT, HTH, THH). So, there are 3 outcomes with two heads.

4. Three heads: This can only happen in one way, which is when all three coins land heads (HHH). So, there is 1 outcome with three heads.

So, if each outcome counts only the number of heads, there are 1 (no heads) + 3 (one head) + 3 (two heads) + 1 (three heads) = 8 outcomes.