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 find the number of possible outcomes for the three positions, we can use the concept of permutations.
In this case, we have 35 members on the committee, and we need to select 3 members for the positions of president, secretary, and treasurer.
To calculate the number of possible outcomes, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n represents the total number of items and r represents the number of items we want to select.
For the position of president, we have 35 candidates to choose from. So we have P(35, 1) possible outcomes.
For the position of secretary, we have 34 remaining candidates after selecting the president. So we have P(34, 1) possible outcomes.
For the position of treasurer, we have 33 remaining candidates after selecting the president and the secretary. So we have P(33, 1) possible outcomes.
To find the total number of possible outcomes for all three positions, we multiply the individual outcomes:
P(35, 1) * P(34, 1) * P(33, 1) = 35 * 34 * 33 = 39,090.
Therefore, there are 39,090 possible outcomes for the three positions in the committee election.