Kinh Nghiệm Hướng dẫn How many ways can a president vice president secretary and treasurer be chosen from a committee of 9 people? 2022

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Video transcript

A club of nine people wants to choose a board of three officers, President, Vice President, and Secretary. Assuming the officers are chosen random, what is the probability that the officers are Marcia for president, Sabita for Vice President, and Robert for Secretary? So to think about the probability of Marcia– so let me write this– President is equal to Marcia, or Vice President is equal to Sabita, and Secretary is equal to Robert. This, right here, is one
possible outcome, one specific outcome. So it’s one outcome out of the total number of outcomes, over the total number of possibilities. Now what is the total number of possibilities? Well to think about that, let’s just think about the three positions. You have President, you have Vice President, and you have Secretary. Now let’s just assume that we’re going to fill the slot of President first. We don’t have to do President first, but we’re just going to pick here. So if we’re just picking
President first, we haven’t assigned anyone to any officers just yet, so we have nine people to choose from. So there are nine possibilities here. Now, when we go to selecting our Vice President, we would have already assigned one person to the President. So we only have eight people to pick from. And when we assign our Secretary, we would’ve already assigned our President and Vice President, so we’re only going to have seven people to pick from. So the total permutations here or the total
number of possibilities, or the total number of ways, to pick President, Vice President, and Secretary from nine people, is going to be 9 times 8 times 7. Which is, let’s see, 9 times 8 is 72. 72 times 7, 2 times 7 is 14, 7 times 7 is 49 plus 1 is 50. So there’s 504 possibilities. So to answer the question, the probability of Marcia being President, Sabita being Vice President, and Robert being Secretary is 1 over the total number of possibilities, which is 1 over 504. That’s the probability.

Nội dung chính

  • Video transcript
  • All Algebra II Resources
  • All Algebra II Resources
  • How many ways can a president a vice president a secretary and a treasurer be chosen from 7 nominated members?
  • How many different ways can a president a vice president and a treasurer be selected?
  • How many different ways can a president vice president secretary and treasurer be chosen from a group of 9 people?
  • How many ways can the president the vice president and the secretary be elected from a group of 10 students *?

All Algebra II Resources

Find the Computing Permutation.

Correct answer:

Explanation:

 

An ice cream vendor sells five different flavors of ice cream. 

In how many ways can you
choose three scoops of different ice cream flavors if order matters?

Correct answer:

Explanation:

There are five ways to choose the first scoop, then four ways to choose the second scoop, and finally three ways to choose the third scoop:

5 * 4 * 3 = 60

There are
5 men and 4 women competing for an executive body toàn thân consisting of :

  • President
  • Vice President
  • Secretary
  • Treasurer
  • It is required that 2 women and 2 men must be selected

    How many ways the executive body toàn thân can be formed?

    Correct answer:

    Explanation:

    2
    men can be selected:

    2 women can be selected out of 4 women:

    Finally, after the selection process, these men and women can fill the executive body toàn thân in
    ways.

    This gives us a total of

    How many ways can a three committee board select the president, vice president and treasurer from a group of 15 people?

    Correct answer:

    Explanation:

    In this problem, order is important because once someone is chosen as a position they can not be chosen again, and once a position is filled, no one else can fill that in mind.

    The presidential spot has a possibility of 15 choices, then 14 choices for vice president and 13 for the treasurer.

    So:

    How many ways can you re-arrange the letters of the word JUBILEE?

    Correct answer:

    Explanation:

    There are 7 letters in the word jubilee, so initially we
    can calculate that there are ways to re-arrange those letters. However, The letter e appears twice, so we’re double counting. Divide by 2 factorial (2) to get .

    How many ways can you re-arrange the letters of the word BANANA?

    Correct answer:

    Explanation:

    At first, it makes sense that there are ways to re-arrange these letters. However, the letter A appears 3 times and the letter N appears twice, so divide
    first by 3 factorial and then 2 factorial:

    In a class of 24 students, how many distinct groups of 4 can be formed?

    Correct answer:

    Explanation:

    To solve, evaluate

    13 rubber ducks are competing in a race. How many different arrangements of first, second, and third place are
    possible?

    Correct answer:

    Explanation:

    There are 3 winners out of the total set of 13. That means we’re calculating

    7
    students try out for the roles of Starsky and Hutch in a new school production. How many different ways can these roles be cast?

    Correct answer:

    Explanation:

    There are 7 potential actors and 2 different roles to fill. This would be calculated as  divided by  , or 42

    How many different 4 letter words can be made out of the letters A, B, C, D, and E?

    Correct answer:

    Explanation:

    Since order matters, use the permutation formula:

    There are 5 letters to choose from (n), and you pick 4 of them (r).

    So there are 120 possible words that can be formed.

    All Algebra II Resources

    How many ways can a president a vice president a secretary and a treasurer be chosen from 7 nominated members?

    Patrick H. There are 5040 different ways a president, vice president, secretary, and treasurer can be selected.

    How many different ways can a president a vice president and a treasurer be selected?

    Correct answer:
    The presidential spot has a possibility of 15 choices, then 14 choices for vice president and 13 for the treasurer.

    How many different ways can a president vice president secretary and treasurer be chosen from a group of 9 people?

    Hence, they can be chosen in 3,024 ways.

    How many ways can the president the vice president and the secretary be elected from a group of 10 students *?

    9! =12×11×10×9×8×7×6×5×4×3×2×19×8×7×6×5×4×3×2×1=12×11×10=1,320.
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