For Problems #1 through #9, consider the following context:The Student Activities & Campus Engagement Office at Saint Patrick's College is reviewing how some organizations and volunteers are being selected for various positions and tasks.

The eight (8) active seniors in the Statistics Club must select three (3) such members to represent the organization at a regional conference.How many ways can this be accomplished, sinceorder doesn't matter?

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The eight (8) active juniors in the Statistics Club must elect three (3) officers - president, vice-president, treasurer - from their class for the following academic year, since it is a tradition that rising seniors serve in these roles.How many ways can this be accomplished, sinceorder does matter?

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The Community Service Council recently received nine (9) similar requests for students volunteers off-campus.The club can immediately fill two (2), but will first satisfy one request and then the second, in that order.How many ways can this be accomplished?

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The Community Service Council recently received nine (9) similar requests for student volunteers off-campus.The club can immediately fill two (2) requests at the same time.How many ways can these requests be filled?

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Thirteen students lined up early to register for the poetry slam.How many ways can the students line up in order?

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A renovated floor of the Student Center contains twelve new small office spaces for student organizations that need physical space.How many ways can these offices be assigned to twelve student groups?

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The Community Service Council has twenty-four (24) volunteers on standby to assist with a natural disaster that impacted the campus.Seven (7) are needed for the same specific task.How many ways can these seven be selected randomly for the same task?

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The Community Service Council has twenty-four (24) volunteers on standby to assist with a natural disaster that impacted the campus.Seven (7) are needed, but will be prioritized for varying tasks so each assignment is different.How many ways can these seven be selected randomly for these variable tasks?

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Bonus:The vintage bulletin board outside the main office for Student Activities and Campus Engagement had an appropriately whimsical holiday theme for Saint Patrick's Day.A block letter title was to read,LUCKY LEPRECHAUN LEGACY, but the student worker accidentally dropped the letters as he was about to thumbtack them onto the bulletin board.He scrambled to gather them into a random pile.In how many distinguishable ways can the twenty-one letters from the three words be collected into one ordered pile, ignoring the spaces?[COMMENTS & HINTS:Remember to express the answer as a counting number,notin scientific notation.The actual number of digits is coincidentally appropriate!]

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