Question

How many $4$ digits numbers can due formed by using the digits $1,2,3,4,5,6,7$ if at least one digit is repeated.

Answer 1

Total no. of digits $=7$

No. of ways $4$ digit numbers can be formed with repetition $=7\times 7\times 7\times 7=2401$

No. of ways $4$ can be formed with repetition $=7\times 6\times 5\times 4=840$

Therefore,

No. of ways $4$ digit numbers can be formed if atleast one digit is repeated $=2401-840=1561$