Question

How many four-digit numbers can be formed where at least two of the four digits are same?​

Answer 1

Answer:

This is a simple problem provided it is approached in the right way.

Total number of 4-digit numbers that can be formed = 9*10*10*10 = 9000

[ First digit in 9 ways {1–9}, subsequent digits in 10 ways {0–9} ].

4 digit Numbers that have different digits (no digits are same)= 9*9*8*7 = 4536

[ First digit in 9 ways {1–9}, Second digit in 9 ways [0–9, exclude first digit], Third digit in 8 ways [0–9, exclude first and second digit] and the Fourth digit in 7 ways [0–9, exclude first, second and third digits].

Numbers that have at least one digit repeated = 9000 - 4536 =4464