The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,…

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:

Accepted Answer

1-digit numbers: $4$ (excluding 0)

2-digit numbers: first digit 4 choices (non-zero), second digit 5 choices: $4\times5=20$

3-digit numbers: $4\times5\times5=100$

4-digit numbers (must be less than 7000, so first digit from $\{1,3\}$ only, since 7,9 would exceed or equal 7000): $2\times5\times5\times5=250$

$$\text{Total} = 4+20+100+250 = 374$$

Solutions · 1