In how many ways can three prizes be given to 10 boys when a boy may receive any number of prizes?

The number of ways in which first prize may be given = 10.
Number of ways in which second prize may be given = 10.
Number of ways in which third prize may be given = 10.
∴  By fundamental principle of counting, the total number of permutations
                                           = 10 x 10 x 10 = 1000
                             ALTERNATIVELY :  n = 10,  r = 3
                              Number of permutations (for repeat case) = n^r = 10³ = 1000.