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JV Stats #5

Combinations, Permutations, and Factorials. JV Stats #5. Handshakes. If everyone in this room shook hands, how many would there be?. Should we try it and count?. Let’s try a smaller example with a few volunteers. Is there a formula?. Combinations. The formula is nCr or Formula.

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JV Stats #5

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  1. Combinations, Permutations, and Factorials JV Stats #5

  2. Handshakes • If everyone in this room shook hands, how many would there be? • Should we try it and count? • Let’s try a smaller example with a few volunteers. • Is there a formula?

  3. Combinations • The formula is nCr or • Formula • This is used when “order doesn’t matter”

  4. Combinations • What are some other examples when the combinations formula can be used?

  5. All-League Team • If Mr. Pines has 9 players he think deserve to be nominated for the All-League team, however only the top 5 will probably make it. • How many ways can he choose his top 5? • Is there a formula for this? Can we use the combinations formula?

  6. Permutations • The formula is nPr • nPr • This is used when “order matters”

  7. Combinations • What are some other examples when the permutations formula can be used?

  8. At the movies • You and 5 of your friends are going to the movies. Once inside the theatre you realize that there are only six seats left in the front row. • How many different ways can you and your friends arrange your seating?

  9. Factorials!!!!!!!!!!!!!! • When you have EXACTLY the same # of things and places, you can use factorials. • Another key word is “arrangements” • The formula is n!

  10. Group Activity • Your assignment for today is to come up with 2 questions for the following: • Combinations,Permutations, and Factorials. • Write the question in complete sentence/s. • Show you answer to each. • Be creative, write them as multiple choice where the distractors are the answers using the wrong formulas

  11. Replacement & Without Replacement • Assume that the letters R.A.N.C.H.O. are in a bag. • If you draw 2 letters, one at a time with replacement, how many different pairs of letters are possible? List them. “order matters” RR,RA,RN,RC,RH,RO,AR,AA,AN,AC,AH,AO,NR,NA,NN,NC,NH,NO,CR,CA,CN,CC,CH,CO,HR,HA,HN,HC,HH,HO,OR,OA,ON,OC,OH,OO 62 = 36

  12. Replacement & Without Replacement • Assume that the letters R.A.N.C.H.O. are in a bag. • Repeat the process but do not replace the letters this time. List the combinations.”order matters” RA,RN,RC,RH,RO,AR,AN,AC,AH,AO,NR,NA,NC, NH,NO,CR,CA,CN,CH,CO,HR,HA,HN,HC,HO,OR,OA,ON,OC,OH 6 x 5 = 30

  13. Replacement & Without Replacement • Assume that the letters R.A.N.C.H.O. are in a bag. • Repeat the process but do not replace the letters this time. List the combinations.”orderdoesnt matter” RA,RN,RC,RH,RO,AN,AC,AH,AO,NC, NH,NO,CH,CO,HO 6C2 = 15

  14. Replacement & Without Replacement • Assume that the letters R.A.N.C.H.O. are in a bag. • If you draw 2 letters, one at a time with replacement, how many different pairs of letters are possible? List them. “order doesn’t matter” RR,RA,RN,RC,RH,RO,AA,AN,AC,AH,AO,NN, NC,NH,NO,CC,CH,CO,HH,HO,OO NO FORMULA

  15. Other types of probability problems • Troy,Paul,Scott,Kevin,Jesus,Jason,Joey, & the guide are going on a white water rafting trip. The boats they ride in only carry 4 people and seating arrangements in each boat does not matter(because they will be thrown out of their seats most likely anyway). How many different ways can the boats be loaded if Kevin and Jason must be together and the guide must be with Scott?

  16. Liars & Cheaters • At Duke University, two students had received A’s in Chemistry all semester. But on the night before the final exam, they were partying in another state and didn’tget back to Duke untilitwas over. Their excuse to the professorwasthattheyhad a flat tire, and theyasked if theycouldtake a make-up test.

  17. Getting What they Deserved • The professor agreed, wrote out a test, and sent the two to separate rooms to take it. The first question(on one side of the paper) was worth five points. Then they flipped it over and found the second question, worth 95 points: “which tire was it?” • How many different ways can they answer? • What was the probability that both students would say the same thing?

  18. 5 card poker hands • What is the theoretical probability of being dealt a 3 of a kind? combinations for other 2 cards 3 of the 4 cards Choices for each of other cards Choices for 1st card All possible 5 card hands

  19. 5 card poker hands • What is the theoretical probability of being dealt a 2 pair?

  20. Easier 5 card poker hands • What is the probability of being dealt all hearts? OR

  21. Easier 5 card poker hands • What is the probability of being dealt no sevens? OR

  22. Easier 5 card poker hands • What is the probability of being dealt all face cards?

  23. Easier 5 card poker hands • What is the probability of being dealt at least 1 club? The opposite of this is to be dealt no clubs Final answer

  24. Group Assignment • Create 4 probability questions based on being dealt 5 cards. • Make sure you have answers to these questions.

  25. Drawing balls from a bucket Let’s assume there are 70 balls in a bucket How many different combinations are possible if you draw 5 balls at a time without replacement? 70C5 = 12,103,014

  26. Drawing balls from a bucket Let’s assume there are 70 balls in a bucket a) What is the probability of matching the exact 5 winning numbers? b) What is the probability of matching exactly 3 of the numbers? c) What is the probability of matching at least one of the winning numbers?

  27. Drawing balls from a bucket Let’s assume there are 70 balls in a bucket

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