Idaho Society of Professional Engineers
Friday Update – 09/29/06
UPCOMING EVENTS:
• October 17, 2006 -
ISPE Southwest Chapter
Noon Meeting
• October 27, 2006 - PE and PS
Examinations - Boise, Idaho
• October 28, 2006 - FS (aka
LSIT) Examination - Boise, Idaho, Pocatello, Idaho, Moscow, Idaho
• October 28, 2006 - FE (aka EIT)
Examination - Boise, Idaho. Pocatello, Idaho, Moscow, Idaho
• February 6 – 10, 2007 –
Idaho Society of Professional Land
Surveyors Conference - Coeur d' Alene Casino - Worley, Idaho
Ethics Forum
Protection of the Public Health and Safety
October 18, 12:30–1:30 PM Eastern
Professional Competence and Qualifications for Practice
November 15, 12:30–1:30 PM Eastern
Honesty and Integrity in Professional Practice
Ethics
Forum registration form
December 12, 1:30–3:00 PM Eastern
EJCDC Contact Documents: Using and Understanding the EJCDC Engineering &
Construction Documents-
Funding Agency Edition
Learn best practices to better use the only pre-approved construction and
engineering services contract documents for use on water and wastewater projects
financed by the USDA/Rural Utilities Service.
Register
early
MATHCOUNTS PROBLEM OF THE WEEK
Can you solve this MATHCOUNTS problem? The answer will appear in next week's
edition of the Friday Update!
Probability Playground
Each of the four digits in the number 2006 is placed on a different card. Two of
the cards are drawn at random without replacement. What is the probability that
the product of the two drawn digits is not zero?
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Lunches for three brothers, Adam, Ben, and Carl are made and the lunchbags are
marked with their names. It is dark when they leave for school. They each pick
up a lunchbag as they go out the door. What is the probability that no one gets
their own lunch?
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Each whole number from 1 through 50 inclusive is written on a disk, and the 50
disks are placed in a bag. Two disks are drawn from the bag at random without
replacement. What is the probability that the number on each disk is a prime
number? Express your answer as a common fraction.
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Each whole number from 1 through 50 inclusive is written on a disk and the 50
disks are placed in a bag. Each whole number from 51 through 100 inclusive is
written on a disk and those 50 disks are placed in a second bag. One disk is
drawn at random from each of the bags. What is the probability that the number
on both disks is a prime number? Express your answer as a common fraction.
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Each whole number from 1 through 100 inclusive is written on a disk and the 100
disks are placed in a bag. Two disks are drawn from the bag at random without
replacement. What is the probability that the number on both disks is a prime
number? Express your answer as a common fraction.
Answer to last week’s MATHCOUNTS problem:
(32 MB) ÷ (2.6 MB/ picture) = 12.3 pictures. There is not enough storage
space to hold 13 pictures so 12 complete pictures can be stored on the storage
card.
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Simon choosing 8 pictures from 10 pictures is the same as not choosing 2
pictures. Counting the ways he does not choose two pictures is a reasonable
strategy. Label the pictures A, B, C, D, E, F, G, H, I, J. There are 9 pictures
that can be paired with A, e.g., AB, AC, AD, AE, AF, AG, AH, AI, AJ. There are 8
pictures that can be paired with B, e.g., BC, BD, BE, BF, BG, BH, BI, BJ. The AB
combination is not included because it has already been counted with pairings
for A. Continuing in this manner there are 7 pairings with C, 6 with D, 5 with
E, 4 with F, 3 with G, 2 with H and 1 with I. The number of ways to not choose 2
pictures is the sum 1 + 2 + ...+ 8 + 9 = 45. Therefore, the number of ways to
choose 8 different pictures from 10 different pictures is 45.
Another way to approach the solution is with a formula. The formula for the
number of subsets that can be chosen from a set is N! ÷ (C! × (N - C)!) where N
is the number of items in the set and C is the number of items in the subset
chosen from the set. Substituting into the formula gives 10! ÷ (8! × (10 - 8)!)
= (10 × 9) ÷ (2 × 1) = 45. There are 45 different sets of 8 pictures that can be
chosen from the set of 10 pictures. The nCr function on many calculators can
also be used to find the number of subsets of a given set.
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There are 8 positions to place the pictures. Simon has a choice of 8 pictures to
be placed in the first position, 7 pictures in the second, 6 pictures in the
third position and so on. There are 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 8! = 40,320
different arrangements of the 8 pictures.
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Marcel appears in 7 pictures and Danika appears in 5 pictures. If they each
appear alone in the pictures there would have to be 7 + 5 = 12 pictures. Since
there are only 10 pictures, Marcel and Danika must appear together in 2 of the
pictures.
If you want to see last week's problem again, click
http://www.mathcounts.org/webarticles/anmviewer.asp?a=900&z=107
Idaho Society of Professional Engineers
PO Box 170239
Boise, ID 83717-0239
208-426-0636
Fax: 208-426-0639
E-Mail: ispe@idahospe.org
Web Site: www.Idahospe.org
Idaho
Society of Professional Engineers
