How many natural numbers that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 7 & 8?
Choose the correct choice from the following answers.
A) 5000 B) 4096 C) 6560 D) 4095 E) 8000
Solution:   We are missing digits 5 and 9 in the question. So we have 8 digits for each position (ones,tens,hundreds,thousands).   The numbers that can be constructed using 8 digits in 4 positions = (8 x 8 x 8 x 8) - 1 (To disregard the case 0000)   = 4096 - 1= 
<gadget id="calculator">4096 - 1</gadget>
<output>4_095</output>
4095   If you have use 10 digits (0 thru 9), you have (10 x 10 x 10 x 10) - 1= 9999 numbers.   Answer 4095.
<result>D</result>
How many natural numbers that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 7 & 8?