A President and Vice- President for a school council are chosen from a hat with the names of all 12 members in the hat. Determine the probability that Nisha and Anne are chosen as President and Vice- President respectively.

Answer Provided: 1/132.

google "permutations"

p(12,2) = 12!/(12-2)! = 12!/10!

= 12 * 11

= 132

To determine the probability that Nisha and Anne are chosen as President and Vice-President respectively, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

First, let's calculate the total number of possible outcomes. Since there are 12 members in the hat, any one of them can be chosen as President. Therefore, there are 12 possible choices for the President.

Next, after the President is chosen, there are 11 remaining members in the hat. Since one of them needs to be chosen as Vice-President, there are 11 possible choices for the Vice-President.

To find the number of favorable outcomes, we consider that Nisha needs to be chosen as President and Anne needs to be chosen as Vice-President. Since there are no restrictions on the order in which we select the President and Vice-President, we can multiply the number of choices for each position. Therefore, there is 1 choice for Nisha to be President and 1 choice for Anne to be Vice-President.

To summarize:
- Total number of possible outcomes: 12 choices for President x 11 choices for Vice-President = 132 outcomes
- Number of favorable outcomes: 1 choice for Nisha as President x 1 choice for Anne as Vice-President = 1 outcome

Finally, to calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 1 / 132.

Therefore, the probability that Nisha and Anne are chosen as President and Vice-President respectively is 1/132.