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 sanwei Posts: 1, Reputation: 1 New Member #1 Apr 15, 2011, 08:00 PM
Find the numbers of codes which can be formed from digits 1 and 0 if they consists 10
Find the numbers of codes which can be formed from digits 1 and 0 if they consists 10 digits.
 jcaron2 Posts: 986, Reputation: 204 Senior Member #2 Apr 15, 2011, 08:30 PM
First let's pretend you only have 1 digit, not 10. How many possibilities are there in that case? 0 or 1. That's 2 possible combinations.

How about if you have 2 digits? 00, 01, 10, or 11. That 4 possible combinations.

What about 3 digits? 000, 001, 010, 011, 100, 101, 110, 111. That's 8 combinations.

Do you see the pattern?

The number of combinations is 2 to the power of the number of digits. 1 digit gives you $2^1$ = 2 different possible combinations; 2 digits gives you $2^2$ = 4 different possible combinations; 3 digits gives you $2^3$ = 8 different possible combinations. So 10 digits would give you $2^{10}$ = 1024 different combinations.

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