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Mayur
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If a gym is open a total of 5 days a week and two different 03 Jun 2004, 20:57
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If a gym is open a total of 5 days a week and two different people work out randomly 2 days per week. What is the probability that both of them will be there on the same day at least once in a given week?



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hallelujah1234
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If a gym is open a total of 5 days a week and two different 03 Jun 2004, 23:41
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1-(5c2*3c2/(5c2*5c2)) = 1-(3/10) = 7/10
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Praetorian
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If a gym is open a total of 5 days a week and two different 06 Jun 2004, 17:10
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anyone wants to answer this
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Mayur
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If a gym is open a total of 5 days a week and two different 06 Jun 2004, 19:49
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The answer given by hallelujah1234 is correct. The explanation is this: -

It says each of the two people visit the gym twice a week.

Person #1 can choose C(5,2) = 10 pairs of days.
Person #2 can choose C(5,2) = 10 pairs of days.

There are 10 x 10 = 100 possible ways they could visit the gym.
Of these 100 ways, in how many of them do #1 and #2 visit on different days?
#1 can visit in any of 10 ways . . . Let's pick one.
Say, he visits on Monday and Tuesday: X X _ _ _
Then #2 can pick two of the other three days: C(3,2) = 3 ways.
So, for each of the 10 choices for #1, there are 3 choices for #2.
Hence, there are 10 x 3 = 30 ways in which they do NOT meet at the gym.
Therefore, there are 100 - 30 = 70 ways in which they DO meet at the gym
and the probability that they will meet at the gym (at least once) is: 70/100 = 7/10.



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