How many four digit numbers can be formed by using the digits $1,2,3,4,5,6,7$, if atleast one digit is repeated?

The numbers that can be formed when repetition of digits is allowed are $7^4=2401.$

The numbers that can be formed when all the digits are distinct when repetition is not allowed are ${}^{7}P_4=840.$

Therefore, the numbers that can be formed when atleast one digit is repeated $=7^4-{}^{7}P_4$

=$2401-840=1561$