SOLUTION: 1. A quiz consists of six multiple choice questions, each with five choices. In how many ways can a student mark the answers to all the questions, markng all of them incorrectly?

Question 408132: 1. A quiz consists of six multiple choice questions, each with five choices. In how many ways can a student mark the answers to all the questions, markng all of them incorrectly?

2. Calculate the number of ways in which four paintings can be awarded first, second, third, and fourth prizes at an art competition in which a total of 30 paintings are displayed.

Found 2 solutions by ewatrrr, richard1234:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
1. A quiz consists of six multiple choice questions, each with five choices.
In how many ways can a student mark the answers to all the questions, markng
all of them incorrectly?
Four ways for each of the 6 questions to mark incorrectly: Note: It is agreed
Ways to mark ALL 6 incorrectly: 4 * 4 * 4 * 4 * 4 * 4
1stQ 2ndQ 3rdQ 4thQ 5thQ 6thQ
(Picturing 'each' of the 4 incorrect responses to '1st question' having
4 unique incorrect responses for 'second question' and 'each' of those case scenarios
having 4 unique incorrect responses for the '3rd question' and so on...)
2. Calculate the number of ways in which four paintings can be awarded first,
second, third, and fourth prizes at an art competition in which a total of 30
paintings are displayed. '30P4' = 30*29*28*27= 657,720 ways
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
1. There are four ways to mark each answer incorrectly, and there are six questions. The number of ways to do so is (they multiply, not add).

2. The order matters here, so the number of ways is 30P4 = 30*29*28*27 = 657,720.
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