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  • In how many ways can 7 different prizes be distributed among 3 students, where each student can receive at most one prize and one student got two prizes?  <div class='qna-option'

In how many ways can 7 different prizes be distributed among 3 students, where each student can receive at most one prize and one student got two prizes?

 

Option: 1

4,032


Option: 2

5,062


Option: 3

4,862


Option: 4

8,208


Answers (1)

best_answer

To calculate the number of ways the 7 different prizes can be distributed among 3 students, where each student can receive at most one prize and one student got two prizes, we can consider the following:

First, we select the student who will receive two prizes. There are 3 students to choose from, so there are 3 options.

Next, we assign the two prizes to the chosen student. There are 7 prizes to choose from for the first prize, and 6 remaining prizes to choose from for the second prize. This can be calculated as 7\times 6= 42 options.

Finally, we distribute the remaining 5 prizes among the other two students. Each of the remaining two students can receive at most one prize, so for each prize, there are 2 students to choose from.
Since there are 5 remaining prizes, this gives us 2^{5}= 32 options.

To calculate the total number of ways to distribute the prizes, we multiply the number of options for each step:

3 \times 42 \times = 4032

Hence, there are 4,032 distinct ways to distribute the 7 different prizes among 3 students, where each student can receive at most one prize and one student got two prizes.

 

Posted by

Irshad Anwar

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