Sets, combinatorics

The digits 3, 4, 6, 9, 0 are used to form four-digit numbers, each digit being used only once. How many of these numbers can be formed?

The digits 3, 4, 6, 9, 0 are used to form four-digit numbers, each digit being used only once. How many of these can be divisible by 3?

The digits 3, 4, 6, 9, 0 are used to form five-digit numbers, each digit being used only once. How many of these can be divisible by 3?

In the final of a swimming competition, 8 competitors compete. If only the top three places count and there is no tie, how many different results can there be?

The ninth grade was asked to enter the hall during the freshman dance with the girls first, followed by the boys. In how many orders can they enter if there are 8 boys in a class of 15?

How many subsets of {m;a;t;h} are there?

Ten of one group ordered soup, 15 ordered second courses. Six people ordered both. How many people are in the group if everyone ordered soup, a second course or both?

Which set operation is the marked part on the Venn diagram?

• 
• 
• 
• 

Which set operation is the marked part on the Venn diagram?

• 
• 
• 
• 

Which set operation is the marked part on the Venn diagram?

• 
• 
• 
•