In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets. more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets. more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes ?
(i) 4 prizes be distributed among 5 students so that no student gets more than one prize can be done in 5P4 = 5!(5−4)!= 5!(1)!=5! ways.
(ii) The first prize can be given away in 5 ways as it may be given to anyone of the 5 students.
The second prize can also be given away 5 ways, since it may be obtained by the student who has already received a prim Similarly, third and fourth prize can be given away in 5 ways.
Hence, the number of ways in which all the prize can be given away = 5×5×5×5=625
(iii) Since any of the 5 students may get all. the prizes. So, the number of ways in whiCh, a student gets all the 4 prizes is 5.
So, the number of ways in which a stude does not get all prizes = 625-5 = 620.
(i) 4 prizes be distributed among 5 students so that no student gets more than one prize can be done in 5P4 = 5!(5−4)!= 5!(1)!=5! ways.
(ii) The first prize can be given away in 5 ways as it may be given to anyone of the 5 students.
The second prize can also be given away 5 ways, since it may be obtained by the student who has already received a prim Similarly, third and fourth prize can be given away in 5 ways.
Hence, the number of ways in which all the prize can be given away = 5×5×5×5=625
(iii) Since any of the 5 students may get all. the prizes. So, the number of ways in whiCh, a student gets all the 4 prizes is 5.
So, the number of ways in which a stude does not get all prizes = 625-5 = 620.
