Total number of different ways that the awards can be distributed is; 150 ways.
- It is clear from the question that the awards and the students are different.
- Now, each student will receive at least one award.
This means that the five different awards could be separated into;
3 + 1 + 1 awards or 2 + 2 + 1 awards.
- Now, for one person to get 3 awards and the other 2 people to get one award each, the number of ways is calculated as;
⁵C₃ × 3! = 60 ways
- Now, for the case where one person is to get 1 award and the other 2 people to get two awards each, the number of ways is calculated as;
((⁵C₂ × ³C₂)/2) × 3! = 90 ways
- Thus; total number of ways the awards can be distributed = 60 + 90 = 150 ways.
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