Question

The number of $4$ digit numbers that can be formed using $1,2,3,4,5,6,7$, if at least one digit is repeated is

• A. $7^4$
• B. ${}^7{C}_4$
• C. $7^4-840$
• D. ${}^7{C}_4\times 4!$

Answer 1

The correct option is C $7^4-840$

Total numbers that can be formed when repetition of digits is allowed
$=7^4$
Total numbers that can be formed when repetition is not allowed
$=7\times 6\times 5\times 4=840$

$\therefore$ The total required numbers $=7^4-840$