Combinatorics (Shai Simonson)

Question

How many n length base 10 numbers are there with at least 3 zeros?

Comments

Rishabh Gupta 2 

number of 1 digit 10 base numbers are 10 :P(pretty obvious)

10¹ = 10 and

9 * 10⁰ is 9

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@Utkarsh What about 2 digit numbers?

You can say that's 100. But this 100 includes 10 1-digit numbers(0 through 9) and 90 2-digit numbers(10 to 99).

So, when you say n-digit number. $10^n$ will include 1-digit numbers, 2- digit numbers ...., n-digit numbers.

In the question you fixed the digits to be n.

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So, when you say n-digit number. 10ⁿ will include 1-digit numbers, 2- digit numbers ...., n-digit numbers

yeah correct but 10ⁿ also includes 2 digit base 10 number(with 0 as first digit) and other numbers till 99

that adds upto 100.

01 is a 2 digit base 10 number and a (single digit) whole number