The number of natual numbers from 1000 to 9999 (both inclusive) that do not have all 4 different digits is

Question

The number of natual numbers from 1000 to 9999 (both inclusive) that do not have all 4 different digits is (A) 4048 (B) 4464 (C) 4518 (D) 4536

Tardigrade Admin · Accepted Answer

Total - All four different =9 × 103-9 ⋅ 9 ⋅ 8 ⋅ 7 OR all 4 digit even number - number of 4 digit even numbers with different digit (4500 - 2296) = 2204.

Q. The number of natual numbers from 1000 to 9999 (both inclusive) that do not have all 4 different digits is

4048

4464

4518

4536

Total - All four different $= 9 \times 1 0^{3} - 9 \cdot 9 \cdot 8 \cdot 7$
OR
all 4 digit even number - number of 4 digit even numbers with different digit
$(4500 - 2296) = 2204.$

Q. The number of natual numbers from 1000 to 9999 (both inclusive) that do not have all 4 different digits is

4048

4464

4518

4536

Total - All four different =9×103−9⋅9⋅8⋅7 OR all 4 digit even number - number of 4 digit even numbers with different digit (4500−2296)=2204.

Total - All four different $= 9 \times 1 0^{3} - 9 \cdot 9 \cdot 8 \cdot 7$
OR
all 4 digit even number - number of 4 digit even numbers with different digit
$(4500 - 2296) = 2204.$