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

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 $= 7^{4} - {}^{7}P_{4}$

= $2401 - 840 = 1561$

Related content