Download presentation
1
Chapter 10 Counting Techniques
2
Permutations Section 10.2
3
Permutations A permutation is an arrangement
of n objects in a specific order.
4
Factorial Notation Factorial Formulas For any counting n
5
Exercises: In how many ways can 4 people be seated in a row?
4 3 2 1 = 4! = 24 If 6 horses are in a race and they all finish with no ties, in how many ways can the horses finish the race? 6 5 4 3 1 = 6! = 720 — — — — — —
6
Exercises: Formula: (n – 1)! In how many ways can 4 people
be seated in a circle? Formula: (n – 1)! (4 – 1)! = 3! = 321 = 6 Notice: The answer is not the same as standing in a row. The reason is everyone could shift one seat to the right (left) but they would still be sitting in the same order or position relative to each other.
7
Permutation Formula The number of permutations of n
objects taking r objects at a time (order is important and n r).
8
Exercise: A basketball coach must choose 4 players to
play in a particular game. (The team already has a center.) In how many ways can the 4 positions be filled if the coach has 10 players who can play any position? 10 nPr 4 = 10 x 9 x 8 x 7 = 5040
9
Assume the cards are drawn
Exercises: Assume the cards are drawn without replacement. In how many ways can 3 hearts be drawn from a standard deck of 52 cards? 13 nPr 3 = 13 x 12 x 11 = 1716 In how many ways can 2 kings be drawn from a standard deck of 52 cards? 4 nPr 2 = 4 x 3 = 12
10
Complementary Counting Principle
11
Exercises: Out of 5 children, in how many ways
can a family have at least 1 boy? n(A) = n(U) – n(A' ) n(at least 1 boy) = 25 – n(no boys(all girls)) = 25 – 1 = 31 Out of 5 children, in how many ways can a family have at least 2 boys? n(A) = n(U) – n(A' ) n(at least 2 boys) = 25 – [n(no boys) + n(1 boy)] = 25 – [1 + 5] = 26 END
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.