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26 Nov 2021, 03:46
Kudos
Bookmarks
In how many ways can 3 different prizes be distributed among 5 students when no student gets all the prizes?
A. \(60\)
B. \(100\)
C. \(120\)
D. \(124\)
E. \(125\)
A. \(60\)
B. \(100\)
C. \(120\)
D. \(124\)
E. \(125\)
26 Nov 2021, 03:47
Kudos
Bookmarks
Official Solution:
In how many ways can 3 different prizes be distributed among 5 students when no student gets all the prizes?
A. \(60\)
B. \(100\)
C. \(120\)
D. \(124\)
E. \(125\)
Each of the three prizes can be assigned to any of the five students, so each prize has 5 options. So, the total number of ways to distribute 3 prizes among 5 students without the restriction is \(= 5*5*5=125\).
This number contains 5 cases when each of the students gets all 3 prizes, so to get the desired number we should subtract these cases from 125. Thus, the final answer is \(125-5=120\).
Answer: C
In how many ways can 3 different prizes be distributed among 5 students when no student gets all the prizes?
A. \(60\)
B. \(100\)
C. \(120\)
D. \(124\)
E. \(125\)
Each of the three prizes can be assigned to any of the five students, so each prize has 5 options. So, the total number of ways to distribute 3 prizes among 5 students without the restriction is \(= 5*5*5=125\).
This number contains 5 cases when each of the students gets all 3 prizes, so to get the desired number we should subtract these cases from 125. Thus, the final answer is \(125-5=120\).
Answer: C
02 Sep 2024, 04:46
Kudos
Bookmarks
1. Requirement: No student gets all the prizes => A student can get no prize, 1 prize or 2 prizes
2. Each prize can be assign to each of 5 students
=> Total number of ways of assignments: \(5 * 5 * 5 = 5^3 = 125\)
3. Number of ways where a student get all the prizes: 5
==> 125 - 5 - 120
Answer is C
2. Each prize can be assign to each of 5 students
=> Total number of ways of assignments: \(5 * 5 * 5 = 5^3 = 125\)
3. Number of ways where a student get all the prizes: 5
==> 125 - 5 - 120
Answer is C
