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October 23rd, 2014, 09:55 PM   #1
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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?
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October 24th, 2014, 02:03 AM   #2
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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.
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October 24th, 2014, 03:05 AM   #3
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Quote:
Originally Posted by nwicole View Post
Q1
Q2
How many integers from 1 to 10,000 , inclusive , are multiples of 5 or 7 or both?
$\displaystyle \textbf{Generally, you need to use }\left\lfloor\frac{1000}{[a,b]}\right\rfloor \text{where [a,b] is the least common multiple of a and b.}\\
\textbf{For 5, you need to divide by 5. For 7, you need to divide by 7. In this case,}\\ \textbf{you need to divide by }5 \times 7 =35$
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October 24th, 2014, 09:24 AM   #4
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Quote:
Originally Posted by prakhar View Post
$\displaystyle \textbf{Generally, you need to use }\left\lfloor\frac{1000}{[a,b]}\right\rfloor \text{where [a,b] is the least common multiple of a and b.}\\
\textbf{For 5, you need to divide by 5. For 7, you need to divide by 7. In this case,}\\ \textbf{you need to divide by }5 \times 7 =35$

so shall I just add (10,000/5)+(10,000/7)- (10,000/35)?

i got it thank you so much
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October 24th, 2014, 11:46 AM   #5
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Quote:
Originally Posted by nwicole View Post
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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