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I have a problem regarding birthdays that involve the possible birthdays a group of 5 people can have within the 7 days of the week.

My solution to this was 5^7 total possibilities, but I'm not sure if that's correct? What intuition is needed for this?

EDIT: So, my issue is I'm not sure how to go about this. I know I should use multiplication principle. However, how does one figure out if it's 5^7, 7^5, 7! (5 times) etc. . . .

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    $\begingroup$ "intuition": the multiplication principle. And, your answer is wrong. $\endgroup$ May 17, 2015 at 15:11
  • $\begingroup$ Please add the [self-study] tag & read its wiki. $\endgroup$ May 17, 2015 at 15:17
  • $\begingroup$ I already am using the multiplication principle. However, in the wrong way. Perhaps it makes more sense that instead of considering it as 7 days a week with 5 people each, (5x5x5x5x5x5x5) it makes more sense the other way around? I just don't know how to determine which one makes more sense really. $\endgroup$
    – user77364
    May 17, 2015 at 15:29
  • $\begingroup$ Consider a simpler problem. What if there were only 2 people? How many possible birthday-day of week combinations could they have? You can count these out manually w/o any math, if you need. Then you can try to scale the solution up. $\endgroup$ May 17, 2015 at 15:43
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    $\begingroup$ ahh. I got 49 options which is 7^2. So . . . . the pattern is just the other way around from what I did then (7^5, not 5^7). If that's correct, thanks for the tip! I'll keep in mind to think of problems simpler $\endgroup$
    – user77364
    May 17, 2015 at 15:52

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So the first person can have his/her birthday on any of the seven days of the week: seven possible outcomes. For the second person, there'd be also seven possibilities, that could occur for each one of the 7 scenarios regarding the birthday of the first person, for a total of $7^2$ possible outcomes. And so on, until you reach your five-person group, which would give you a combined sample space of $7^5$ possible outcomes.

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  • $\begingroup$ Please read our policies for [self-study] questions on the tag's wiki. Be cautious of providing full answers. $\endgroup$ May 17, 2015 at 15:53
  • $\begingroup$ OK. I'll erase. $\endgroup$ May 17, 2015 at 15:55

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