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After the fifth grade math class
I teach olympiad mathematics. Ask me all these questions in the future.

1, Xiao A, Xiao B and Xiao C have made an appointment to sign up for one of the four events in the school sports meeting: long jump, high jump, 100 meter run and 200 meter run. Q: How many different situations will appear in the registration results?

2. 1, 2, 3, 4, 5, 6***, how many four-digit odd numbers can be formed?

3. In natural numbers, use two digits as the minuend and one digit as the minuend. * * * How many different subtraction formulas can be formed?

4. How many numbers can the numbers1,2, 3, 4, 5, 6, 7 and 8 make up?

① ① Three digits?

② Three even numbers?

③ Three-digit even number without repetition?

(4) Three-digit, eight-digit and non-repetitive digits?

⑤ A three-digit even number with eight digits and no repeated digits?

5. The telephone number of the city is six digits, the first digit cannot be 0, and the rest digits can be any one from 0 to 9, and the digits with different digits can be repeated. So, how many telephones can this city accommodate at most?

Xiaoming borrows books from the library. There are 65,438+050 different foreign language books, 200 different science and technology books and 65,438+000 different novels in the library. So, how many different ways does Xiaoming borrow books?

7. There are three balls in one pocket and eight balls in the other pocket, all of which have different colors. Q:

How many different ways to listen to a ball from two pockets?

② How many different ways are there to take out a small ball from each of the two pockets?

8. There are 6 different picture books and 7 different books on the bookshelf. Take at most two (can't help but take them). How many different ways are there?

9. Ten keys open ten locks, but I don't know which key opens which lock. Q: How many times can I try to unlock the lock and key at most?