Q Apply
- 8 P 6 or 6 P 2
Determine which value is greater.- 9 C 6 or 9 P 6
41. 9 P 7 or 9 P 2
44. nC 5 or UC 8
4 2 - 10P 3 o r 8 ^4- 7 C 4 or 8 C 5
Fi g u r e 1- Think About a Plan Draw four points like those in Figure 1. Draw line
segm ents so th at every p o in t is jo in ed to every o th er point. How m any
line segm ents did you draw? How m any segm ents w ould you n e e d to
join each p o in t to all the o thers in Figure 2?
- How m any points are th ere in Figure 2?
- Should you use com binations or p erm u ta tio n s to find th e n u m b e r of
segm ents th a t join pairs of points?
- a. Lena w ants a passw ord th a t uses th e 4 letters of h er nam e. How m any
p erm u ta tio n s are possible using each letter only once?
b. W riting Is creating a passw ord b ase d on your n am e a good idea? Explain
your reasoning. - License Plates In one state, a regular license plate h as a tw o-digit n u m b e r th a t is
fixed by county, th e n one letter, an d th e n four one-digit num bers.
a. How m any different license plates are possible in each county?
b. Suppose th ere are 92 counties in th e state. How m an y license plates are possible
in th e entire state?
Find the num ber of arrangements o f letters taken three at a tim e that can be
formed from each set o f cards.
49.51.AE F G H I JReasoning Explain w hether each situation is a perm utation problem or a
combination problem.- A locker contains 8 books. You select 3 books at random. How m any different sets of
books can you select? - You take 4 books out of th e school library to read during spring vacation. In how
m any different orders can you re ad th e 4 books? - Media The call signs of radio a n d television stations in th e U nited States generally
begin w ith th e letter W east of th e M ississippi River an d th e letter K w est of the
Mississippi. R epetition of letters is allowed.
a. How m any different call signs are possible if each station uses a W or K followed
by 3 letters?
b. How m an y different call signs are possible if each station uses a W or K followed
by 4 letters?
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5k-j Lesson 12-6 Permutations and Combinations^767