6. At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention." In how many different ways could the two awards be given out?
Question
- At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention." In how many different ways could the two awards be given out?
Solution 1
To solve this problem, we need to use the concept of permutations.
Step 1: Determine the number of ways to award the "Best in Show". Since there are 5 finalists, there are 5 possible dogs that could win this award.
Step 2: Determine the number of ways to award the "Honorable Mention". After the "Best in Show" has been awarded, there are only 4 dogs left. So, there are 4 possible dogs that could win this award.
Step 3: Multiply the results of Step 1 and Step 2 to get the total number of ways the two awards could be given out.
So, the total number of ways is 5 * 4 = 20 ways.
Solution 2
To solve this problem, we need to use the concept of permutations.
Step 1: Determine the number of ways to award the "Best in Show". Since there are 5 finalists, there are 5 possible dogs that could win this award.
Step 2: Determine the number of ways to award the "Honorable Mention". After the "Best in Show" has been awarded, there are only 4 dogs left. So, there are 4 possible dogs that could win this award.
Step 3: Multiply the results of Step 1 and Step 2 to get the total number of ways the two awards could be given out.
So, the total number of ways is 5 * 4 = 20 ways.
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