12- 5 Samples and Surveys
Quick Review
You can obtain inform ation ab o u t a population of people
by surveying a sm aller p art of it, called a sam ple. The
sam ple should be representative of the population. An
unrepresentative sam ple or a poorly w orded q u estio n can
result in bias.Ex a m p l e
A survey asks, "Should Plainville make itself proud by
building a beautiful n ew library?” Is the question biased?
The question is biased. The w ords proud a n d beautiful m a k e
it clear th at th e answ er is expected to b e yes.A
Ex e r c i se s
Determ ine w hether the sam pling m ethod is random,
systematic, or stratified. Tell w hether the m ethod will give
a good sam ple. Then write an unbiased survey question
for the situation.- Movies An interview er outside a movie th eate r asks
every third p erso n in line w h e th e r he or she will see
m ore or fewer m ovies in th e com ing year. - Student Government Ten randomly chosen
stu d en ts in each class (freshm an, sophom ore, junior,
a n d senior) are asked w hom they su p p o rt for student
council president.
12- 6 Permutations and Combinations
f .............................................................. mmW
Quick Review
If there are m ways to m ake a first selection a n d n ways to
m ake a second selection, th e n th ere are m • n ways to m ake
the two selections.
A perm utation is an arran g em en t of objects in a specific
order. The n u m b e r of p erm u tatio n s of n objects arranged r
at a time, „Pr, equals (n f r),.
A com bination is a selection of objects w ithout regard to
order. The n u m b er of com binations of n objects ch o sen r at
a time, nCr, equalsEx a m p l e
In how m any ways can you ch oose 3 p eop le to serve on a
com m ittee out of a group of 7 volunteers?
The order does n o t matter, so this is a com bination problem.
7 C3 = 31 ( 7 - 3 ~j! = W r i t e u s in g fa c to r i a l s.
_ 7,6,5,4,3,2, l Write the factorials as
(3*2* 1)(4 • 3 • 2 • 1) products.= 35 Simplify.
There are 35 ways to choose 3 p eople out of a group of 7................ A
Ex e r c i s e s
Find the num ber o f perm utations.- 9 P 5 23. 3 P 2 24. 8 P 3
- 5 P 2 26. 6 P 4 27. 7P 2
Find the num ber of com binations. - 8 C 2 29. 9 C 4 30. 5 C 3
- 6 C 3 32. 7 C 3 33. 5 C 4
- Side Dishes You can choose any 2 of the following
side dishes w ith your dinner: m ashed potatoes, cole
slaw, french fries, applesauce, or rice. How m any
different com binations of side dishes can you choose? - Talent Show There are 8 groups participating in a
ta le n t show. In h ow m an y different orders can the
groups perform? - Clothing You have 6 shirts, 7 pairs of pants, and
3 pairs of shoes. How m any different outfits can
you wear?
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