A committee will elect a president, a secretary, and a treasurer. If the committee consists of 35 members, how many possible outcomes for the three positions can occur? (Note that no member can be elected in two positions.)
To determine the number of possible outcomes for the three positions, we can use a concept called permutations.
A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations for selecting three members from a committee of 35.
To calculate the permutations, we can use the formula for permutations of n objects taken k at a time, which is:
P(n, k) = n! / (n - k)!
Where "!" denotes factorial, which means multiplying a number by all the positive integers less than itself down to 1.
In this problem, the number of possible outcomes for the president position is 35 (since any committee member can be elected), for the secretary position it's 34 (as one member has already been elected as president), and for the treasurer position, it's 33 (as two members have already been elected).
So, to find the total number of possible outcomes, we multiply these numbers together:
Total number of outcomes = 35 * 34 * 33
Calculating this expression gives us:
Total number of outcomes = 39,270
Therefore, there are 39,270 possible outcomes for the three positions in the committee election.
To find the number of possible outcomes for the three positions, we can use the concept of permutations.
For the president position, there are 35 members to choose from.
For the secretary position, there are 34 remaining members to choose from after the president has been chosen.
For the treasurer position, there are 33 remaining members to choose from after both the president and secretary have been chosen.
To calculate the total number of outcomes, we multiply these three numbers together:
35 * 34 * 33 = 39,090
Therefore, there are 39,090 possible outcomes for the three positions.