Podcast
Questions and Answers
In how many ways can 4 prizes be distributed among 5 students when no student gets more than one prize? Total ways: ______ ways.
In how many ways can 4 prizes be distributed among 5 students when no student gets more than one prize? Total ways: ______ ways.
120
When a student may get any number of prizes, the total ways to distribute 4 prizes among 5 students is ______ ways.
When a student may get any number of prizes, the total ways to distribute 4 prizes among 5 students is ______ ways.
625
If we want to find the ways in which no student gets all the prizes, we first calculate the total ways, which is 625, and then subtract the ways in which a student gets all prizes, which is ______ ways.
If we want to find the ways in which no student gets all the prizes, we first calculate the total ways, which is 625, and then subtract the ways in which a student gets all prizes, which is ______ ways.
5
The final calculation for the ways no student receives all prizes is ______ ways.
The final calculation for the ways no student receives all prizes is ______ ways.
When calculating the distribution of prizes, the outcome when no student gets more than one prize is calculated using ______ factorial.
When calculating the distribution of prizes, the outcome when no student gets more than one prize is calculated using ______ factorial.
Flashcards
Permutation
Permutation
The number of possible arrangements of objects where order matters.
Combination
Combination
The number of ways to choose a subset from a set, where order doesn't matter.
Distributing Prizes (No Repetition)
Distributing Prizes (No Repetition)
The number of ways to distribute 4 prizes among 5 students if no student receives more than one prize.
Distributing Prizes (Repetition Allowed)
Distributing Prizes (Repetition Allowed)
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Distributing Prizes (Excluding All Prize Winner)
Distributing Prizes (Excluding All Prize Winner)
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Study Notes
Distributing Prizes Among Students
- Four prizes are to be distributed among five students. There are three scenarios to consider:
Scenario (i): No student gets more than one prize
- The total number of ways is 5! = 120 ways.
Scenario (ii): Students can get any number of prizes
- The total number of ways is 625 ways.
Scenario (iii): No student gets all the prizes
- The total number of ways is 625 - 5 = 620 ways.
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