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Pennant Fever
Review
Adam Johnson
Nate Levin
Ian Olsen
Unit Problem
 The good guys and the bad guys each
have 7 games to play. Based on each of
their winning records ( .62 good guys and
.6 bad guys) we must determine the
chances each team has to win the
pennant.
Key Topics
 Combinations
 Permutations
 Pascal’s Triangle
 Factorials
 Binomial Theorem
Factorials
 Multiplication pattern
 Sign is “!”
 Multiply the coefficient of “!” by every
whole number below it, excluding
numbers zero and below.
 4!=4*3*2*1=24
Combinations
 nCr
 n!/(n-r)!*r!
 Order doesn’t matter
 Bowls of ice cream
 Answer question #1 on worksheet now
Question #1
 12C1 x 7C1 x 4C1 x 5C1=?
 12x7x4x5=1680
 When r value is equal to one, the final answer
of the value is equal to the n value
 (12!/(12-1)!*1!)*(7!/(7-1)!*1!)*etc…
 5C1=5
 5*4*3*2*1=120
 120/4!=5
Permutations
 nPr
 n!/(n-r)!
 Order does matter
 Cones of ice cream
 Answer question #4 on worksheet now
Question #4
 22P7=?
 22!/(22-7)!=859,541,760
 22!=1.12E21
 Answer question #2
Question #2
 Explain the difference between 10P7 and
10C7
 Well P will obviously be larger as the
order of the combinations matter,
increasing the total number of
possibilities.
Question #2 (Continued)
 We can see the steps that are different in
the previous slide that make 10P7 and
10C7 different.
 Due to the difference in order mattering
or not, the final answer will change
drastically.
Pascal’s Triangle
 Shows the binomial coefficient
 Shows nCr values
Binomial Theorem
 Finds the coefficients of binomial
 Answer question #8
Question #8
 (2X+3)^5