COUNTING METHODS REVIEW AND SELF TEST

Suggestions for this self exam:
[A] Study Rolf (sections 6.3, 6.4, 6.5), but then keep your book closed during this entire test
[B] Method choice buttons (colored ovals) for each problem are scripted to show the correct choice when the mouse arrow moves over them. Hence, keep your mouse restrained until you have thought out your response.
[C] Then type in your integer answer to the problem in the box provided, rounding to the nearest dollar: this page doesn't do arithmetic, so write "24" instead of "6 * 4" or "4!". You may check each answer.
[D] The 3 counting principles are reviewed in your text (Rolf):
 The MULTIPLICATION PRINCIPLE is in section 6.3 (Pg 455) If Task A can be done in m ways, and Task B can be done in n ways, then both tasks can be done in (m n) ways The PERMUTATIONS PRINCIPLE is in section 6.4 (Pg 468) If k objects are selected from a larger collection of m objects, those k objects can be lined up in a row in P(n,k) ways, where P(n,k) = n(n-1)(n-2)(n-3).......(n-k+1), that is, the product of k integers starting downward from n The COMBINATIONS PRINCIPLE is in section 6.5 (Pg 479) The number of subsets of size k which can be selected from a larger set of size n is C(n,k) = [ P(n.k) divided by k! ]

  Two soups, 5 meat dishes, and 3 desserts are on the menu of Neptune restaurant. How many different meals are possible, each consisting of one soup, one meat dish, and one dessert? Choosemethodfirst⇢   Then enter an integer answer to question   ⇢

 In how many ways can the letters of the word CREAM be arranged?  Choosemethodfirst⇢   Then enter an integer answer to question    ⇢

  An ATM pin number consists of 4 digits, such as 1111, 0011 or 2345. How many such pin numbers are possible? Choosemethodfirst⇢   Then enter an integer answer to question    ⇢

  An ATM pin number consists of 4 DIFFERENT digits, such as 1234, 8765, or 2345. In this version of the previous problem, 0011 and 1111 are NOT allowed. How many such pin numbers are now possible? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  A woman's wardrobe contains 2 blazers, 4 blouses, and 3 skirts. Assuming any combination looks fine, how many "outfits" are available in this wardrobe, each consisting of a blazer, a skirt, and a blouse? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  Five finalists are to be chosen from 1O contestants in a contest. How many such sets of 5 finalists are possible if the finalists are ranked? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  In how many ways can the Supreme Court render a 5-4 decision in support of the death penalty? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  Five people must line up in a row for a group photo. How many different such group photos are possible? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  One way to answer a 1O-question true-false test is : T T T T T T T T T T. Another way to answer this same test is : T T T T T T T T T F. All together, how many ways are there to answer the questions on this test? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  Five awards (1st, 2nd, 3rd, 4th, and 5th place) are to be chosen for the five entrants in a pie contest. In how many ways can these awards be assigned? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

 How many 5-card poker hands are possible when dealing from a 52-card deck?  Choosemethodfirst⇢   Then enter an integer answer to question    ⇢

  A 1O-member club must elect 4 officers: a president, vice-president, secretary, and treasurer. How many different election results are possible? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  A 5-person committee must be chosen from a 10-member club. How many different such committees are possible? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  How many different arrangements are possible for 7 books on a shelf? Choosemethodfirst⇢   Then enter an integer answer to question    ⇢

  In how many ways can each of 1O numbered billiard balls be assigned to one of the 2 side pockets? Each pocket is big enough to hold all 1O balls. Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢

  Five non-permanent seats in the UN Security Council are to be selected from among 10 countries. How many such sets of 5 nations are there? Choosebestmethodfirst⇢   Then enter an integer answer to question    ⇢  