Permutations And Combinations

Question
CBSEENMA11014041

How many 3 digit numbers are there without repetition?

Solution

Digits available are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Total number of digits = 10
Number of digits used = 3
                           
Number of filling box (z) = 9              [∴ If 0 is put in there, it becomes a two digit number]
rightwards double arrow                       m = 9
Number of ways of filling box (y) = 9                        (3  Repetition is not allowed)
rightwards double arrow                     n = 9
Number of ways of filling box (x) = 8                         (3  Repetition is not allowed)
rightwards double arrow                      p = 8
∴ The number of 3 digit numbers or numbers between 100 and 1000
                               = m x n x p = 9 x 9 x 8 = 648     
                                     



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