Permutations And Combinations

Question
CBSEENMA11014120

Find the number of 4-digit numbers in which at least one digit is repeated.

Solution

Number of digits = 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Number of digits used = 4
Number of permutations in which at least one digit is reveresed = x - y      ...(i)
where                x = number of permutations when any digit may be repeated any number of times,
                        y = number of permutations when no digit is repeated.
From part (a),     x = 9000
From part (b),      y = 4536.
Hence, the number of 4-digit numbers in which at least one digit is repeated.
                            = 9000 - 4536 = 4464

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