Question

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:

Answer 1

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The number of natural number less than 7000 are in the form of 1 digit , 2 digit , 3 digit and 4 digit number

[Zero can't be filled in first place]

The number of 1 digit natural numbers less than 7000 is 4

The number of 2 digit natural numbers less than 7000 is 4 × 5 i.e 20

The number of 3 digit natural numbers less than 7000 is 4 × 5 × 5 i.e 100

The number of 4 digit natural numbers less than 7000 is 2 × 5 × 5 × 5 i.e 250

Only two digits i.e 1 and 3 can be filled in first place of four digit number less than 7000

$\sf \hookrightarrow Total \: number \: of \: numbers = 4 + 20 + 100 + 250 \\ \\ \sf \hookrightarrow Total \: number \: of \: numbers = 374$

Hence , 374 natural numbers less than 7000 can be formed by using the digits 0, 1, 3, 7, 9 when repetition of digits allowed

Answer 2

Step-by-step explanation:

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