October 23rd, 2014, 08:55 PM  #1 
Newbie Joined: Oct 2014 From: los angeles Posts: 17 Thanks: 0  counting problem
Q1 Two dice are rolled , one blue and one red. how many outcomes have either the blue die 3 or an even or both? Q2 How many integers from 1 to 10,000 , inclusive , are multiples of 5 or 7 or both? 
October 24th, 2014, 01:03 AM  #2 
Senior Member Joined: Mar 2012 Posts: 571 Thanks: 26 
Without just giving you the answer, the point of the questions is to think about inclusion/exclusion. Think about a Venn diagram with two overlapping circles. If you want to count the number of elements of the two sets, you need to 1) count the members of each 2) subtract the overlapping area, to avoid doublecounting. Whereas if the circles don't overlap you can simply count the members of both sets and add.

October 24th, 2014, 02:05 AM  #3  
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  Quote:
\textbf{For 5, you need to divide by 5. For 7, you need to divide by 7. In this case,}\\ \textbf{you need to divide by }5 \times 7 =35$  
October 24th, 2014, 08:24 AM  #4  
Newbie Joined: Oct 2014 From: los angeles Posts: 17 Thanks: 0  Quote:
so shall I just add (10,000/5)+(10,000/7) (10,000/35)? i got it thank you so much  
October 24th, 2014, 10:46 AM  #5 
Senior Member Joined: Mar 2012 Posts: 571 Thanks: 26  

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