Permutations And Combinations

Question
CBSEENMA11014036

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.


Solution


Number of digits available = 5

Number of places for the digits = 3.
Number of ways in which place (x) can be filled = 5
                           m = 5
Number of ways in which place (y) can be filled = 5    (∵  Repetition is allowed)
                            n = 5 
Number of ways in which place (z) can be filled = 5    (∵ Repetition is allowed)
                             p = 5
∴ By fundamental principle of counting, the number of 3-digit numbers formed.
                           = m x n x p = 5 x 5 x 5 = 125

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