Three coins are tossed. How many ways are there to get more than 2 tails, exactly 2 heads, only 1 tail.
Thanks in advance for the help!
To solve this problem, we will use the concept of combinations and permutations.
1. Ways to get more than 2 tails:
To find the number of ways to get more than 2 tails, we need to consider the outcomes where we have 3 tails as well as the outcomes where we have 2 tails.
- For 3 tails, there is only 1 possible outcome (TTT).
- For 2 tails, we need to choose one of the three coins to not be a tail. This can be done in 3 ways (HTT, THT, TTH).
Hence, there are a total of 1 + 3 = 4 ways to get more than 2 tails.
2. Ways to get exactly 2 heads:
To find the number of ways to get exactly 2 heads, we need to consider the outcomes where we have 2 heads and 1 tail.
- We need to choose 2 out of the 3 coins to be heads. This can be done in 3C2 = 3 ways.
- The remaining coin will be a tail.
Hence, there are a total of 3 ways to get exactly 2 heads.
3. Ways to get only 1 tail:
To find the number of ways to get only 1 tail, we need to consider the outcomes where we have 1 tail and 2 heads.
- We need to choose 1 out of the 3 coins to be a tail. This can be done in 3C1 = 3 ways.
- The remaining 2 coins will be heads.
Hence, there are a total of 3 ways to get only 1 tail.
In summary:
- There are 4 ways to get more than 2 tails.
- There are 3 ways to get exactly 2 heads.
- There are 3 ways to get only 1 tail.