The number of natural numbers less than 7,000

Question:

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

  1. 250

  2. 374

  3. 372

  4. 375


Correct Option: , 2

Solution:

2 ways for $\mathrm{a}_{4}$

Number of numbers $=2 \times 5^{3}$

Required number $=5^{3}+2 \times 5^{3}-1$

$=374$

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