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

!

( )!

nnPr

n r

• Permutations are ordered arrangements of objects. The number of permutations of r objects taken from a set of n objects is given by:

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

!

! !( )!

nPr nnCr

r r n r

• Combinations are unordered selections of objects. The number of combinations of r objects taken from a set of n objects is given by:

1 2 3

!

! ! ! !k

n

n n n n

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?

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)