Results 1 to 2 of 2

Math Help - Permutations and Combinations

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    1

    Exclamation Permutations and Combinations

    1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?
    2. I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?
    3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?
    4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
    How many ways can 4 toppings be selected where:

    a. All the toppings are vegetables
    b. All the toppings are meat
    c. There is only cheese on the pizza
    d. There are 2 vegetables, 1 meat and 1 cheese
    e. There are 3 meats and 1 cheese.
    What's your favorite combo?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,865
    Thanks
    744
    Hello, gtzfynestbabiigurl!

    1) I am going to choose 6 students out of 15 to be mentors.
    How many ways can a group 6 be selected?
    There are: . _{15}C_6 \:=\:{15\choose6} \;=\;5,005 ways.

    2) I've decided that the mentor group should be made up of 3 girls and 3 boys.
    Of the 15 students, 9 are girls and 6 are boys.
    How many ways can I form the group
    There are: . \left(_9C_3\right)\left(_6C_3\right) \;=\;{9\choose3}{6\choose3} \;=\;1,680 ways.


    3) State and multi-state lotteries are common in the U.S.
    To win a typical lottery, you must match 6 numbers between 1 and 40.
    How many different combinations are possible?
    There are: . _{40}C_6 \:=\:{40\choose6} \:=\:3,838,380 possible combinations.

    What does that say about the chances of winning the lottery?
    A lottery is a penalty for being weak in mathematics.


    1) A pizza shop offers the following toppings:
    8 different vegetables, 5 different meats, and 4 different cheeses.
    How many ways can 4 toppings be selected where:

    a) All the toppings are vegetables.
    There are: . {8\choose3} \:=\:{8\choose4} \:=\:70 ways.

    b) All the toppings are meat.
    There are: . {5\choose4} \:=\:5 ways.

    c) All the toppings are cheese.
    There is: . {4\choose4} \:=\: 1 way.

    d) There are 2 vegetables, 1 meat and 1 cheese.
    There are: . {8\choose2}{5\choose1}{4\choose1} \:=\:560 ways.

    e) There are 3 meats and 1 cheese.
    There are: . {5\choose3}{4\choose1} \:=\:40 ways.

    What's your favorite combo?
    White truffles, Beluga caviar, dusted with saffron . . . Just kidding!

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. DNA permutations and combinations
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 8th 2010, 03:45 PM
  2. combinations and permutations
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 1st 2010, 03:49 PM
  3. I need help in Permutations and Combinations
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 23rd 2010, 04:04 PM
  4. combinations of permutations?
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 10th 2009, 07:21 PM
  5. Combinations and permutations
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 18th 2008, 05:10 PM

Search Tags


/mathhelpforum @mathhelpforum