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How many ways can a group of 20 be selected from 25 individuals?

Jane, Shane, Elaine, Blaine, Zane, Wayne, and Dane must form a line. Jane insists on being first and refuses to stand next to anyone other than Zane or Wayne. Given Jane’s demands, how many ways can all 7 people form a line?

After submitting your exam, go to Week 13 Module > Exam 4 Handwritten Work and follow the instructions. Your handwritten work must be uploaded within 15 minutes of submitting the exam. Submitting your handwritten work with clearly labeled steps and calculations is a vital part of the online exam process.  Your handwritten work gives me the opportunity to pinpoint mistakes, identify concepts in need of clarification, and award partial credit where deserved. You will not receive full credit if you do not submit your handwritten work.

A catering company offers 4 different appetizers, 6 different meats, and 3 different pastas. How many ways can Daphne choose 2 different appetizers, 3 different meats, and 1 pasta to be served at her wedding?

How many ways can you choose an appetizer, a main dish, and a dessert from a menu with 5 different appetizers, 7 different main dishes, and 3 different desserts? 

Determine whether each of the following scenarios involve permutations or combinations. (a) How many ways can a group of 5 people be selected from 12 people in a class? [a] (b) How many ways can a president and vice president be chosen from a committee of 30 members? [b] (c) How many ways can the letters A, B, C, D, and E be arranged? [c] (d) How many ways can you choose 7 out of 13 friends to attend a party? [d] (e) How many ways can 4 people arrange themselves in a line for a photo? [e]

Pourquoi est-il important pour les journalistes de vérifier leurs sources avant de publier une information, et quelles conséquences pourraient survenir s’ils ne le font pas ?

During your patient’s physical therapy session, you practice floor to stand transfers.  With verbal cueing, your patient requires 30% physical assistance to safely execute the transfer.  What is the level of assistance you will document?

What are people experiencing when they expect that society will treat them in one way and they perceive that they are not getting what they expected?

What is the most appropriate sequencing for a physical therapist to perform when assisting a person in a manual wheelchair through a doorway that opens toward them?