Permutations And Combinations

Question
CBSEENMA11014117

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

Solution

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) = nr = 103 = 1000.
                                         

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Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.