Download presentation

Presentation is loading. Please wait.

Published byStephan Burdick Modified over 2 years ago

1
Counting Techniques 1

2
Sequential Counting Principle Section 10.1 2

3
Tree Diagrams Tree Diagrams are used to display all the possible outcomes of a situation. T H T H H T 3

4
Sequential Counting Principle SCP If an event can occur in m ways and a second event can occur in n ways, then the sequence of two events can occur in m x n ways. 4

5
SCP Fundamental Counting Principle If an event can occur in m ways, and then a second event can occur in n ways, and then a third event can occur in r ways, and so on, then the sequence of events can occur in m n n r … ways. 5

6
Exercise: A bag contains 6 brown marbles and 3 white marbles. You are asked to draw 3 marbles from the bag without replacement. In how many ways can you draw 2 brown and 1 white in that order? 6 x 5 x 3 = 90 1 st B2 nd B 1 st W 6

7
Exercise: In how many ways can 1 woman and 1 man, in that order, be selected from 5 women and 6 men? 5 x 6 = 30 7

8
Exercise: How many different sets of 3 initials can be made from the letters of the English alphabet? Hint:AAA is different from BBB. 26 x x = 17,576 8

9
Exercise: The Good Taste Restaurant has 7 entrees, 6 vegetables, and 9 desserts on its menu. If you want to order 1 entree, 1 vegetable, and 1 dessert, how many choices do you have? 7 x 6 x 9 = 378 9

10
In Connecticut, auto license plates carry 3 digits followed by 3 letters. a. How many arrangements are possible for the 3 letters? b. How many arrangements are possible for the 3 numbers? c. How many different license plates can be made using 3 numbers followed by 3 letters? Exercise: a. 26 x x = 17,576 b. 10 x x = 1000 c. 17,576 x 1000 = 17,576,000 10

11
Social Security numbers consist of nine digits. a. If the first digit cannot be a 0, how many Social Security numbers are possible? b. How many Social Security numbers are possible if there are no restrictions? Exercise: 9 x 10 8 = 900,000,000 10 9 = 1,000,000,000 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11

12
12

13
You are expected to be familiar with a standard deck of playing cards. Standard deck 52 cards Black 26Red 26 13 Spades ♥ 13 Hearts ♣ 13 Clubs ♦ 13 Diamonds 12 Face Cards (Jack, Queen, & King) Black 6Red 6 3 Spades ♥ 3 Hearts ♣ 3 Clubs ♦ 3 Diamonds 40 Non - Face Cards (A -10) Black 20Red 20 10 Spades ♥ 10 Hearts ♣ 10 Clubs ♦ 10 Diamonds 13

14
Note: the Ace will be considered to be a one. There are four suits: Clubs, Diamonds, Spades, and Hearts in a deck of cards. END 14

Similar presentations

OK

Today Today: Reading: –Read Chapter 1 by next Tuesday –Suggested problems (not to be handed in): 1.1, 1.2, 1.8, 1.10, 1.16, 1.20, 1.24, 1.28.

Today Today: Reading: –Read Chapter 1 by next Tuesday –Suggested problems (not to be handed in): 1.1, 1.2, 1.8, 1.10, 1.16, 1.20, 1.24, 1.28.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on financial performance analysis Ppt on nepali culture Ppt on cse related topics Ppt on data abstraction in java Ppt online download mp3 Ppt on business cycle Ppt on meeting skills Ppt on product specification template Ppt on online shopping cart project Ppt on cross-sectional study limitations