The number of 4 different book combinations you can choose from 6 books is;
6C4 =
6!/[4!(6-4)!] =
15 combinations of 4 different books.
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There are 26 different letters that can be chosen for each letter. There are 10 different numbers that can be chosen for each number. Since each of the numbers/digits that can be chosen for each of the six "spots" are independent events, we can multiply these combinations using the multiplicative rule of probability.combinations = (# of different digits) * (# of different digits) * (# of different digits) * (# of different letters) * (# of different letters) * (# of different letters) = 10 * 10 * 10 * 26 * 26 * 26 = 103 * 263 = 1000 * 17576 = 17,576,000 different combinations.
There are millions of possible combinations.
10
10 Combinations (if order doesn't matter). 3,628,800 Possiblilities (if order matters).
There are just 5,005.There are 10C6 = 210 combinations with 6 different numbers.There are 10C5 = 252 combinations with 5 different numbers. One of these needs to be duplicated and the one to be duplicated can be chosen in 5 ways so there are 1260 of these.There are 10C4 = 210 combinations with 4 different numbers. Either one of them appears three times or two are doubled. That can be done in 10 ways so there are 2,100 of these.There are 10C3 = 120 combinations with 3 different numbers. Either one of them appears 4 times, or one twice and another three times, or all three appear twice. That can be done in 10 ways so there are 1,200 of these.There are 10C2 = 45 combinations with 2 different numbers. Either one of them appears 5 times, or one twice and another four times, or both three times. That can be done in 5 ways so there are 225 of these.There are 10C1 = 10 combinations with just 1 number repeated six times.Add these together.