Hey everyone, please explain how to do these...
1. Numbers are formed from the digits 1, 2, 3, 3, and 7 at random. In how many ways can they be arranged to form a number greater than 30 000? (Answer is 72).
My thinking: In that question, I understand that the first number must be a 3, 3, or 7. After that number has been chosen, there are 4 other options for the next, 3 for the next, 2 for the next and 1 for the last. the double 3's can be swapped, so I'd divide by 2. I get 36.
2. A group of n people sit around a circular table. How many arrangements are possible if k people sit together? (Answer: (n-k+1)!/k!
My thinking: k people sit together, so I can consider that group of people as one person. The amount of people is now equal to n-k+1 (n-k for the people not in the group, and +1 for the group itself). Seeing as the first person (or group) can sit anywhere, the amount of arrangements of people should be equal to (n-k+1-1)! = (n-k)!.
3. How many different arrangements are possible if 3 letters are randomly selected from the word CHALLENGE and arranged into 'words'?
My thinking: I could do this if there weren't any double letters. How do I handle the double letters in the scenario? Some 3 letter words will have double letters, some wont.
1. Numbers are formed from the digits 1, 2, 3, 3, and 7 at random. In how many ways can they be arranged to form a number greater than 30 000? (Answer is 72).
My thinking: In that question, I understand that the first number must be a 3, 3, or 7. After that number has been chosen, there are 4 other options for the next, 3 for the next, 2 for the next and 1 for the last. the double 3's can be swapped, so I'd divide by 2. I get 36.
2. A group of n people sit around a circular table. How many arrangements are possible if k people sit together? (Answer: (n-k+1)!/k!
My thinking: k people sit together, so I can consider that group of people as one person. The amount of people is now equal to n-k+1 (n-k for the people not in the group, and +1 for the group itself). Seeing as the first person (or group) can sit anywhere, the amount of arrangements of people should be equal to (n-k+1-1)! = (n-k)!.
3. How many different arrangements are possible if 3 letters are randomly selected from the word CHALLENGE and arranged into 'words'?
My thinking: I could do this if there weren't any double letters. How do I handle the double letters in the scenario? Some 3 letter words will have double letters, some wont.
