155S4.7.notebook
February 10, 2010
MAT 155­DY1 and DY2
Section 4.7 Counting ­ Factorials, Permutations, Combinations
Sep 16­1:36 PM
Feb 8­7:31 AM
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155S4.7.notebook
February 10, 2010
Feb 8­9:24 AM
Feb 8­9:29 AM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/5. Calculate the factorial: 5!.
195/8. Calculate the permutation: 24P4.
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/6. Calculate the factorial: 8!.
195/10. Calculate the combination: 52C2.
Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/14. Find the probability of winning: Select the six winning numbers from 1, 2, ,3,…, 58, 59.
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/16. Find the probability of winning: Select the five winning numbers from 1, 2, ,3,…, 36, 37.
Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/18. DNA (deoxyribonucleic acid) is made of nucleotides, and each nucleotide can contain any one of these nitrogenous bases: A (adenine), G (guanine), C (cytosine), T (thymine). If one of those four bases (A, G, C, T) must be selected three times to form a linear triplet, how many different triplets are possible? Note that all four bases can be selected for each of the three components of triplets.
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
195/20. If a byte is defined to be a sequence of 8 bits and each bit must be a 0 or 1, how many different bytes are possible? Are there enough different bytes for the characters that we typically use with a computer? Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
196/22. In designing an experiment involving a treatment applied to 12 test subjects, researchers plan to use a simple random sample of 12 subjects selected from a pool of 20 available subjects. How many different simple random samples are possible? What is the probability of each simple random sample in this case?
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
196/24. You have just started your own airline company named Air Me. So far, you have one plane for a route connecting Austin, Boise, and Chicago. One route is Austin­Boise­Chicago and a second route is Chicago­Boise­Austin. How many total routes are possible if service is expanded to include a total of eight cities?
Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
196/26. In a test of a gender­selection method, 14 babies are born and 10 of them are girls.
(a) Find the number of different possible sequences of genders that are possible when 14 babies are born.
(b) How many ways can 10 girls and 4 boys be arranged in a sequence?
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
196/26. In a test of a gender­selection method, 14 babies are born and 10 of them are girls.
(c) If 14 babies are randomly selected, what is the probability that they consist of 10 girls and 4 boys?
(d) Does the gender­selection method appear to yield a result that is significantly different from a result that might be expected by random chance?
Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
196/28. Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. For example, the letters TAISER were included in newspapers on the day this exercise was written. How many ways can the letters of TAISER be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting an arrangement of the given letters.
Sep 16­1:36 PM
Section 4.7 Counting – Factorials, Permutations, and Combinations
197/30. A typical “combination” lock is opened with the correct sequence of three numbers between 0 and 49, inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try?
Sep 16­1:36 PM
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155S4.7.notebook
February 10, 2010
Section 4.7 Counting – Factorials, Permutations, and Combinations
197/32. A carton contains 12 eggs, 3 of which are cracked. If we randomly select 5 of the eggs for hard boiling, what is the probability of the following events?
(a) All of the cracked eggs are selected.
(b) None of the cracked eggs are selected.
(c) Two of the cracked eggs are selected.
Sep 16­1:36 PM
Feb 10­12:21 PM
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