Ask questions and get helpful answers.

I am super confused with permutations and combinations. I just don't see when you are supposed to use each one, and when you aren't supposed to use either.

Our homework was to correct our tests, and I did quite poorly. I tried to fix some of these, so could someone check my answers?

1. In how many ways can 10 people be seated around a circular table?

I really don't get this. On one of homework problems, there was a question like this and the answer was 1 way. I put that on my test, and it was wrong. The only other way I could think to do this was 10! (10 factorial) or 3628800
When would there be only 1 way?

2. There are 6 red bean bags, 5 blue bean bags, and 3 green bean bags in a container. How many ways can 4 bean bags be selected so that:
A) all 4 are red?
B) 2 are blue and 2 are green?
C)exactly 3 are red?

I don't even know how this one would be solved..

3. A license plate for a certain state has 4 digits followed by 2 letters. How many different plates are there if the letters may be repeated but the digits may not?

The only way I could think of to do this would be:

P(6,4)C(6,2)=360 x 15=5400

And that was the wrong answer..

4. Using only the letters {R, S, T, U, A, B, C, D, E}, how many 6-letter codes are possible in which the following is true?
A) Letters can't be repeated.
B) Letters can be repeated.
C) The first letter is a vowel and Letters can't be repeated.
D) The first letter is a vowel and Letters can be repeated.

I thought the answers would be C(9,6), P(9,6), C(8,6), P(8,6) but I got them all wrong. How do you do this?

It would really help me if someone would check these, or show me how to do some of them.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
7 answers
  1. It would really help me if someone could check these. Please?

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. In a very general explanation,
    in a permutation the order or the position of your arrangement matters,
    while in a combination the order does not matter.

    e.g. Suppose from a class of 25 students, 6 are to be chosen to form a mathteam
    The order in which they are chosen does not matter, so that would be a combination.

    On the other hand if those 6 students are to become experts in different areas of math on the team, that would be a permutation.

    1. This is one of those special cases.
    I will asssume that there is no specific order or special chairs to be filled.
    So let's fill the first chair, that would be 10 ways, the second in 9 ways, etc.
    so that would be 10! ways, right?
    Now suppose everybody got up and moved to the chair on their left, and then sat down. Would the arrangement of people sitting around the table have changed? NO!
    Now think of how many ways they could do this? Could they not do this 10 times, each time resulting in the original arrangement?
    So the 10! ways has to be divided by 10, giving you 9! ways.

    3. for the license plate digits may not be repeated, but letters may.
    Can the plate start with a 0? I will assume it can.
    so the first 4 numbers are 10*9*8*7
    followed by 2 letters which would be 26*26

    so the number of plates is 10*9*8*7*26*26

    4. you have 9 different letters, of those arrange 6, (the order matters)

    a) the number of ways would be 9*8*7*6*5*4

    b) they can be repeated, so 9*9*9*9*9*9
    or 9^6

    c) 3 ways to fill the first spot with a vowel, after that anything goes without repeating the letters

    so no of ways = 3*8*7*6*5*4

    d) only change is 3*9*9*9*9*9

    Let me think about #2, it seems like it should be a probability question
    which would be P(9,6)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. the very last line of "which would be P(9,6)"
    should have come after 4.a) to read

    " a) the number of ways would be 9*8*7*6*5*4
    which would be P(9,6)"

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  4. 2. I am a bit mystified by the wording.
    They are using the word "selected" which suggests a combination, in other words, the order does not matter
    in a) there is only one way for 4 bags to be red, namely RRRR

    b) by the same thinking there is only one way for 4 bags to be 2 blue and 2 red,
    BBRR (BRRB would be the same since order does not matter)

    c) exactly 3 of the 4 bags must be red, meaning that the 4th could be either blue or green
    which would be 2 ways: RRRB or RRRG

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  5. Oh ok, I get it. But i have one more question.

    Why are there always more ways when you use a permutation? Wouldn't you think that you would have more ways when you used a combination since the order doesn't actually matter? I don't know if that makes sense to you. It's kind of bugging me

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  6. suppose from you 5 friends you "choose" 3 to ride in your car.
    That would be C(5,3) = 10

    now suppose you pick 3 people to sit in the passenger seat, the rightrear seat and the leftrearseat.
    that would be 5*4*3 or P(5,3) = 60 ways

    notice the permutation is more.

    Another way to look at it:
    suppose you pick one of the 10 combinations from my example.
    once you have selected the 3 people you want you could now fill the
    frontseat, rearleft and rearright seats in 3*2*1 or 6 ways
    And of course we could do these 6 arrangements for each of our 10 choices, giving us a total of 60 arrangements.

    (I am still puzzled by #2. Are you studying probability questions yet?)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  7. (fog)(-2)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Similar Questions

  1. math 1 question

    Simplify the following expression: 5^2 - 4 / 5 +2 is it 3 or 26.2, i don't know which one, im confused.

  2. math

    The formula for the area A of the triangle is A=1/2BH, where B is the length of the base, and H is the height. Solve the equation for B. I don't know how I'm supposed to be able to figure this out?

  3. chemistry

    how many "particles in solution" will form from each sucrose (C12H22O11) molecule added to water? Explain. I don't understand where I am supposed to start... What do I need to know to do this problem? thank you

  4. pre algebra

    Write rules for using absolute value to compare two integers. BE sure to take all of the possible combinations in to account. __ I don't know what to write?

  5. Chemistry

    The reaction of hydrochloric acid (HCl) with ammonia (NH3) is described by the equation: HCl + NH3 → NH4Cl A student is titrating 50 mL of 0.32 M NH3 with 0.5 M HCl. How much hydrochloric acid must be added to react completely with the ammonia? A. 6.4 mL

  6. math

    If three dice are tossed, their sum could be 7. What is the probability of this? I'm guessing it's something to do with combinations?? I wrote down all the combinations of it equaling 7: 3, 3, 1 // 4, 2, 1 // 1, 5, 1 So I thought that since there are five

  7. earth science

    PLZ HELP which is a possible sequence in the life cycle of a massive star supernova, star, black hole, planetary nebula, super red giant, protostar super red giant, protostar, nebula, star, neutron star, supernova planetary nebula, super red giant,

  8. Chemistry

    Classify the possible combinations of signs for a reaction's ∆H and ∆S values by the resulting spontaneity. A) Spontaneous as written at all temperatures. B) Spontaneous in reverse at all temperatures. C) Spontaneous as written above a certain

  9. Maths

    A super-Fibonacci sequence is a list of whole numbers with the property that, from the third term onwards, every term is the sum of all the previous terms. For example, 1, 4, 5, 10, ... How many super-Fibonacci sequences with 1 involve the number 2016? A.1

  10. Chem?

    Which of these elements can't have an expanded octet in a Lewis structure? P,O,Br,N,S,C,B,Si I think its O,C,B,N. Are elements that don't have a d oribial arent supposed to be included?

Still need help?

You can ask a new question or browse existing questions.