Question:
In how many ways can 4 prizes be distributed among 5 student when.
1. no student get more than 1 prize.. 2. a student may get any no. of prizes. 3. no student get all the prizes
Answer:
(i) Here the prizes are to be distributed. First prize can be distributed in 5 ways, second prize can be distributed in 4 ways and so one.
Total number of ways = 5 × 4 × 3 × 2 = 5! = 120.
(ii) Here, five choices are there for each prize.
Total number of ways = 5 × 5 × 5 × 5 = 54 = 625.
(iii) The number of ways in which we can give four prizes among five students when no student gets all the prices = number of ways in which any student can get any number of prices – the number of ways in which one student gets all the prizes. = 625 – 5 = 620. T
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