Problem 1064 A club wishes to select a presid... [FREE SOLUTION]

Chapter 33: Problem 1064

A club wishes to select a president, vice-president and treasurer from five members. How many possible slates of officers are there if no person can hold more than one office?

Short Answer

Expert verified

There are 60 different possible slates of officers that can be selected from the five members, with no person holding more than one position. This is calculated using the permutation formula \(P(5, 3) = \frac{5!}{(5-3)!} = \frac{120}{2} = 60\).

Step by step solution

Understand the problem

In this problem, we need to choose a president, a vice-president, and a treasurer from five members, with no repetition. This is a problem of permutations since the order of chosen members matters (A president is different from a vice-president or treasurer).

Use the permutation formula

The permutation formula, denoted as P(n, r), is given by: P(n, r) = n! / (n - r)!, where n is the total number of elements, r is the number of elements chosen, and ! denotes the factorial of a number. In this exercise, we have n = 5 (members) and r = 3 (president, vice-president, and treasurer).

Calculate the permutation

Plug in the values of n and r into the permutation formula: P(5, 3) = 5! / (5 - 3)! = 5! / 2!

Evaluate the factorials

Find the factorial values for the numerators and denominators: 5! = 5 脳 4 脳 3 脳 2 脳 1 = 120 2! = 2 脳 1 = 2 Now, divide the factorial values: P(5, 3) = 120 / 2 = 60

Interpret the result

There are 60 different possible slates of officers that can be selected from the five members, with no person holding more than one position.

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91影视

A club wishes to select a president, vice-president and treasurer from five members. How many possible slates of officers are there if no person can hold more than one office?

Short Answer

Step by step solution

Understand the problem

Use the permutation formula

Calculate the permutation

Evaluate the factorials

Interpret the result

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