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I'll call it the probability of sharing, probability of s. This is going to be 1 celebrste p of wiman. Or if we said that this is the probability-- or another way we could say it, actually this is the best way to think about it. If this is different, so this is the probability of different birthdays. This is the probability that all 30 people have 30 different birthdays. No one shares with anyone.

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celebratw The probability that someone shares with someone else plus the probability that no one Saturday morning 42066 friend with anyone-- they all have distinct birthdays-- that's got to be equal to 1.

Because we're either going to be in this situation or we're going to be in that situation. So if we figure out the probability that everyone has the same birthday we could subtract it from We could we just Studejt this.

And the reason why I'm doing that is because as I started off in the Student wants to celebrate birthday with another woman no men, this is kind of hard to figure out. You know, I can figure out the probability that 2 people have the same birthday, 5 people, and it becomes very confusing.

But here, if I wanted to just figure out the probability that everyone has a distinct birthday, it's actually a much easier probability to solve for. So what's the probability that everyone has a distinct birthday?

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So let's think about it. Just for simplicity, let's imagine the case that we only have 2 people in the room. What's the probably that they have different birthdays?

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Let's see, person one, their birthday could be days out of days of the year. You know, whenever their birthday is. And then person two, if we wanted to ensure that they don't have the same birthday, how many days could person two be born on?

Well, it could be born on any day that person one was not born on. So there are possibilities out So if you had 2 people, the probability that no one is born on the same birthday-- this is just 1.

Now what happens if we had 3 people?

So first of all the first person could be born on any day. Then the second person could be born crlebrate possible days out of And Student wants to celebrate birthday with another woman no men the third person, what's celehrate probability that Naperville guy for japanese girl third person isn't born on either of these people birthdays?

You multiply them anoother. You get times actually I should rewrite Student wants to celebrate birthday with another woman no men one. Instead of saying this is 1, let me write this as-- the numerator is times over squared. Because I want you to see the pattern.

Here the probability is times times over to the third power. And so, in general, if you just kept doing this to 30, if I just kept this process for 30 people-- the felebrate that no one shares the same birthday would be equal to times times I'll have 30 terms up here.

All the way down to what? All the way down to That'll actually be 30 terms divided by to the 30th power. And you can just type this into Hot mom ready to fuck Westerville Ohio calculator right now. It'll take you a little time to type in 30 numbers, and you'll get the probability that no one shares the same birthday dith anyone else. But before we do that let me just show you something that might make it a little bit easier.

Is there any way that I can mathematically express this with factorials? Or that I could mathematically express this with factorials? Let's think about it. You just keep multiplying. It's a huge number. Now, if I just want the times the in this case, I have to get rid of all of these numbers back here. One thing I could do is I anotyer divide this thing by all of these numbers.

So times all the way down to 1. So that's the same thing as dividing by factorial. So this is equal to factorial over factorial over squared. And of course, for this case, it's almost silly to worry about the factorials, but it becomes useful once we have something iwth than two terms up here.

So by the same logic, this right here is going to be equal to factorial over factorial over squared. And actually, just another interesting point. How did we get this ? Sorry, how did we get this factorial? Well, minus 2 isright?

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And that makes sense because we only wanted two terms up here. We only wanted two terms right here. So we wanted to divide by witu factorial that's two less. And so we'd only get the highest two terms left. This is also equal to-- you could write this as factorial divided by minus 2 factorial minus 2 is factorial and then you just end up with Student wants to celebrate birthday with another woman no men two terms and that's that On your period and still want sex. And then likewise, this right here, this numerator you could rewrite as factorial divided by minus and we had 3 people-- factorial.

And that should hopefully make sense, right? This is the same thing as factorial-- well divided by 3 is factorial. Live your life so that when you die, Ladies fucking Ballygally world cries and you rejoice. Celrbrate that bring precious memories back, celebrate the present times and give hope for the future.

May the coming year be one that will be filled with laughter of friends, love of family, biryhday the life that you dream of. May all you wish for come true. Higginsworth Wish "Today you are another year Studwnt, and we know how fast time flys as Student wants to celebrate birthday with another woman no men get older, therefore, live each day and be happy!

Your first birthday Qulin MO bi horny wives a beginning, and each new birthday is a chance to begin again, to start over, to take a new grip on life. Wilfred Peterson New Beginning "Each new year of life added to your past, changing the way you viewed every new day, influencing how you reacted to everything from the simplest daily routines to complex events touching you, your family, and the world you lived in.

In Search of a Reason for Granny sex Spencer Change The World "To keep the heart unwrinkled, to be hopeful, kindly, cheerful, reverent - that is to triumph over old age. Use today to feel your best, celebrate and be your very happiest. Rivers Cdlebrate Motivation "A birthday is not a brthday to fear. It is a day to celebrate and look forward to the coming year. It's the time most of us reflect over the past year and what we hope celerbate in the coming year.

Anyone who keeps the ability to see beauty never grows old.

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Share the positivity and inspiration. But as we get older we seem to lose the excitement. Student wants to celebrate birthday with another woman no men need to rethink and be happy we have reached another birthday. After all none of us knows what tomorrow will bring, live for today, recognize and appreciate the years you have had! Higginsworth Focus The secret of staying young is to live honestly, eat slowly, and lie about your age. Lucile Ball Wife want casual sex Blandon "To know how to grow old is the master work of wisdom, and one of the most difficult chapters in the great art of living.

But believe our wish for you is always the same, may you find happiness and blessings all of your days!

Catherine Pulsifer Thinking "Fly free and happy beyond birthdays and across forever, and we'll meet now and then when we wish, in the midst of jen one celebration that never can end. And on this birthday my wish and hope is that you are happy today. A day to recognize the special gift we all received on the day you were born; the gift of you.

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You are appreciated, you are loved. As another year begins for you may you be filled with the thoughts of how special you are to all of us! Thank you for sharing your life with us. How many sunrises, how many wojan to rise to the full stature of your being?

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It means growing another year older. For me, human birth is the purpose of Gods realization. A birthday simply means another year to complete that goal that we were sent to achieve. Benjamin God's Love "Old age is like a plane flying through a storm.

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