You and your mom enter a drawing with 3 different prizes. The prizes are awarded at random.
If a total of 9 people entered the drawing, in how many ways can you win first prize and your mom win second prize?
Since the prizes are awarded at random, each person has an equal probability of winning any of the three prizes.
To calculate the number of ways you can win first prize and your mom can win second prize, we can break it down into steps:
Step 1: Determine the number of ways you can win first prize.
Since there are 9 people in total, there are 9 possible winners for the first prize. Therefore, there are 9 ways you can win first prize.
Step 2: Determine the number of ways your mom can win second prize.
After you have won first prize, your mom is one of the remaining 8 people who can still win a prize. Therefore, there are 8 ways your mom can win second prize.
Step 3: Calculate the total number of ways you can win first prize and your mom can win second prize.
To calculate the total number of ways, we multiply the number of ways in each step: 9 (ways you can win first prize) * 8 (ways your mom can win second prize) = 72.
So, there are 72 ways you can win first prize and your mom can win second prize.