My Math Forum counting problem

 Number Theory Number Theory Math Forum

 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. Thanks from nwicole
October 24th, 2014, 02:05 AM   #3
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 Originally Posted by nwicole Q1 Q2 How many integers from 1 to 10,000 , inclusive , are multiples of 5 or 7 or both?
$\displaystyle \textbf{Generally, you need to use }\left\lfloor\frac{1000}{[a,b]}\right\rfloor \text{where [a,b] is the least common multiple of a and b.}\\ \textbf{For 5, you need to divide by 5. For 7, you need to divide by 7. In this case,}\\ \textbf{you need to divide by }5 \times 7 =35$

October 24th, 2014, 08:24 AM   #4
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 Originally Posted by prakhar $\displaystyle \textbf{Generally, you need to use }\left\lfloor\frac{1000}{[a,b]}\right\rfloor \text{where [a,b] is the least common multiple of a and b.}\\ \textbf{For 5, you need to divide by 5. For 7, you need to divide by 7. In this case,}\\ \textbf{you need to divide by }5 \times 7 =35$

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
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 Originally Posted by nwicole so shall I just add (10,000/5)+(10,000/7)- (10,000/35)? i got it thank you so much
So long as you discard the remainders, yes.

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