Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is _______ . [2023]

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Solution

Q.
Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is _______ . [2023]

Ans.
(2997)

Number starting with 2 and 3 = $2 \times 6^{4}$

Number starting with 40 = $6^{3}$

Number starting with 420, 422, 423, 424, 427 = $5 \times 6^{2}$

Similarly, number starting with 4290 = 6

$Total = 2 \times 6^{4} + 6^{3} + 5 \times 6^{2} + 6 + 3 = 2997$

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