You and your mom enter a drawing with 3 different prizes. The prizes are awarded at random.If a total of 8 people entered the drawing, in how many ways can you win first prize and your mom win second prize?A.2B.8C.1D.6SUBMITarrow_backPREVIOUS
Question
You and your mom enter a drawing with 3 different prizes. The prizes are awarded at random.If a total of 8 people entered the drawing, in how many ways can you win first prize and your mom win second prize?A.2B.8C.1D.6SUBMITarrow_backPREVIOUS
Solution
The problem can be solved by using the concept of permutations.
Step 1: Determine the total number of ways to win the first prize. Since there are 8 people in the drawing, there are 8 ways to win the first prize.
Step 2: Determine the total number of ways to win the second prize. After the first prize has been awarded, there are now 7 people left in the drawing. Therefore, there are 7 ways to win the second prize.
Step 3: Since we are interested in the scenario where you win the first prize and your mom wins the second prize, we multiply the number of ways to win the first prize by the number of ways to win the second prize.
So, 8 ways (for the first prize) * 7 ways (for the second prize) = 56 ways.
However, since the problem is asking specifically for the scenario where you win first and your mom wins second, we don't consider all 56 scenarios, but only one specific scenario.
So, the answer is C. 1.
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