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13. Seven-Cards are dealt off a standard 52-card deck and lined up in a row: How many different Line- ups are there that all cards are black or all cards are face c...

Question

13. Seven-Cards are dealt off a standard 52-card deck and lined up in a row: How many different Line- ups are there that all cards are black or all cards are face cards.

13. Seven-Cards are dealt off a standard 52-card deck and lined up in a row: How many different Line- ups are there that all cards are black or all cards are face cards.



Answers

Drawing Cards How many different 13-card hands include the ace and king of spades?

And this problem. We are learning about probability specifically about the probability of selecting cards. So let's first review what we have. We're told that we have 13 card hands and remember, a full deck is 52 and what we need is we need to know how many combinations are there to get exactly seven spades in my hand. And something to note here is we're not worried about the order. I don't have to worry about when I select the spades or if I'm replacing them. All I need to know is I need to get seven spades at the end of the process. So this is called an N choose K scenario where we're choosing how many things we want out of a total right. We want the seven space out of 13 card hand. So we're going to say that our functions see of 13 7, right, 13 cards in my hand and I want seven is equal to 13 factorial over 13, minus seven factorial time seven factorial. And this is a known way to do this. There is a equation for you to follow. But what this is saying is we're going to take 13 times, 12 times, 11 times, 10 times, nine times, eight times seven factorial. And that's going to continue until we reach the certain point. We're going to divide that by six times five times, four times, three times, two times, one again times seven factorial. So when you put that into a calculator, which I know is a very big number, we get 1716. So what does that mean? With the conditions were given, there are exactly 1716 ways to get exactly seven spades in my hand. So I hope that this problem helped you understand a little bit more about probability and how we can think through understanding a problem like this.

Giving us a 2 52 playing cards. Many did select five guards. In a way. There are three Red Guards Andi to black coat, so total number off cards in each group is 26 because there are 26 bread and 26 placards. So the combination form this 2063 indoor 2062 Will you was formula and see our physical toe in factorial divided by n minus r factorial into our Victoria. So 2063 into 26 c to WIZIG were to win this expectable really 5 26 minus to fool you into three factorial into 26. Factorial divided with 26 minus two factorial in tow to Victoria. So this is given by doing this expecto really by 23 factory Lindo So factorial in 26 with 30 year divided by when they were factorial in tow. Two factorial in ST equals really 625 into 24. Divided by three into two into one into 2016 to 25 divided by doing do when, so this would come out to be. This becomes 13 32664 24. So my answer is get for five triple zero

It's given that in 52 playing cards we have selected five card so in two Taylor bays that can be a cool off. All five cards are black. How many black cars are there in two playing cards? We have Anything will do 26 Black Guards. Order doesn't matter here, and every guard is likely either. Glove Orel Spirit So possible Number of combinations are 2065. So NCR is given by in Victoria the Barbarian minus R factorial in tow. R factorial So 26 c five is important to open this expecto deal. But when the six minus Phi pictorial into five factorial well, this expect ordeal. Dubai 21 factorial into five Victoria. Is it going to 2600.85 into 24. 23 into 20 toe into 21 Factorial do. I didn't but dont even factorial into five into four into three into two into one. The 21 for total My one factorial is canceled by 5 25 on this is 24 from answer is six by 780

This problem wants us to calculate the probability of being no kings when drawing 13 cards with no replacement for a standard deck of cards. Eso these This is ah, Israel dependent events depending on the draw before. So we're gonna have 13 fractions or 13 probabilities. Okay, we're going to find the pattern here. So the first draw is out of 52 cards and there are 48 cards which were not kings and therefore kings in the debt. And then as we draw, uh, our denominators denominator will count down. 52 51 50 49 48 7654321 40. Okay, And then our memories will count down as well. It's our last number will be 36 and we can Ah, simple like counting in multiply like this were used factorial so you can just plug this into the calculator on the way. I would type this in is 48 factorial and we wanted to stop at 36. So we just divided by 35 pictorial have everything less than 36 cancel in the denominator will have 52 factorial and then divided by 39 factorial. So you want to cancel everything? Less than 40. Okay. And then punched that into a calculator and we'll get a probability of 0.30 20.304 which is around, uh, 38.4%. Okay. Thank you.


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