Question

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?

Answer 1

Answer:

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

Answer 2

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 from the chits.

What is Permutations?

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

Here, Total candidates = 10

       Number of selection = 4

The number of ways =  ¹⁰P₄

                                  = (10X9X8X7) = 5040

Thus, there are total 5040 ways to select 4 member out of 10.

Learn more about Permutations from:

https://brainly.com/question/1216161

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