Question
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
