Transcript 3.4 Additional Topics in Probability and Counting

3.4 Additional Topics in Probability and Counting
• Important Concepts
– Permutations
– Combinations
3.4 Additional Topics in Probability and Counting
• Clara, Amanda, Nakita, Morgan, Keanna, Kylie, Alexa, and
Kaleigh are about to start the 400 meter individual medley
at the 2010 Class A Nebraska State Track Meet. In how
many ways can these runners finish the race?
Factorial Notation:
n! = n∙(n – 1)∙(n – 2)∙(n – 3)∙…∙3∙2∙1
• A little league baseball coach needs to select 9 players
from his 12-member roster for tomorrow’s starting lineup.
How many starting lineups can the coach create?
3.4 Additional Topics in Probability and Counting
• Permutations are ordered arrangements of
objects. The number of permutations of r
objects taken from a set of n objects is given by:
n!
nPr 
(n  r )!
3.4 Additional Topics in Probability and Counting
• Douglas Reynholm, president of Reynholm Industries,
must decide which three members of his IT department
will attend a convention in Las Vegas Nevada. The IT
staff include Roy, Moss, Jen, and Richmond. How many
options does Douglas have?
3.4 Additional Topics in Probability and Counting
• Combinations are unordered selections of
objects. The number of combinations of r
objects taken from a set of n objects is given by:
nPr
n!
nCr 

r ! r !(n  r )!
3.4 Additional Topics in Probability and Counting
• Johnny has 8 marbles in his bag – 3 blues, 2 greens, 2
reds, and 1 white. How many distinguishable
permutations of the 8 marbles are possible?
n!
n1 ! n2 ! n3 ! nk !
where n1 + n2 + n3 + … + nk = n
3.4 Additional Topics in Probability and Counting
• Practice:
#16 p. 174
#20 p. 174 (Skiing)
#26 p. 175 (Archaeology Club)
#32 p. 175 (Jury Selection)
#43 p. 176 (Jukebox)
#48 p. 176 (Financial Shape)