In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don’t have an office).

Part A: First, the four officers are chosen. In how many ways can 4 of the 10 candidates be chosen to be president, vice president, secretary, and treasurer? Is this a combination or a permutation?

Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board members. In how many ways can they be chosen?

Part C: The chorus decides to choose the 2 at-large board members from the 6 remaining candidates randomly. What is a fair way to do this?

A) 10P4 = 5040, permutations

B) 6C2 = 15

C) assign them numbers and use a random table to choose two numbers

Or, use ballots. Write their names on chits, shuffle the chits and randomly pick two chits. Select the names on the chits

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: