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Fast Counting (The Counting Principle)

Hey, wait!

Phone numbers can't start with 911!  Hmm... this is a problem!  So, there will be less than 8 million phone numbers.  But, how many is that?

How about if we figure out how many phone numbers DO start with 911... and subtract them out?

Let's see...  They have to start with 911...

So, lock these down:

9 1 1 __ __ __ __ ... Now, it's like the first three digits don't exist. Ignore them! ... How many possibilities are here? ... 10 * 10 * 10 * 10 = 10,000

So, how many phone numbers are there that

a )don't start with a 0 or 1
b )don't start with 911

8,000,000 - 10,000 = 7,990,000

(By the way, we also can't start with 555 or 411, but let's not get ridiculous here.  It's just a math problem!)

 

YOUR TURN:

If your state lottery has you select 6 numbers from
1 - 48...  How many different ways can you make your ticket?