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

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

Permutations and Combinations

Solution:

Total - All four different $=9 \times 10^3-9 \cdot 9 \cdot 8 \cdot 7$
OR
all 4 digit even number - number of 4 digit even numbers with different digit
$(4500 - 2296) = 2204.$