How many ways can 3 prizes be distributed among 4 students so that each student may receive any number of prizes?

Text Solution

Answer : (i) 24 (ii) 64 (iii) 60

Solution : (i) The 1st prize can be given to anyone of the 4 girls in 4 ways. <br> Similarly, the second prize can be given in 3 ways and the 3rd prize can be given in 2 ways. <br> `therefore " the required number of ways"=(4xx3xx2)=24.` <br> (ii) 1st prize can be given in 4 ways, 2nd prize can be given in 4 ways and the 3rd prize can be given in 4 ways. <br> `therefore " the required number of ways"=(4xx4xx4)=64.` <br> (iii) Number of ways in which a girl does not get all the prizes = (number of ways in which a girl may get any number of prizes) - (number of ways in which a girl gets all the prizes) <br> `=(64-4)=60.`