![]() ![]() ![]() So for each of these 30 scenarios, you have four people who you could put in chair number three. To have four people standing up not in chairs. And now if you want to say well what about for the three chairs? Well for each of these 30 scenarios, how many different people could you put in chair number three? Well you're still going So you have a total of 30 scenarios where you have seated six You have five scenarios for who's in chair number two. Someone in chair number one and for each of those six, Or another way to think about it is there's six scenarios of So that means you haveįive out of the six people left to sit in chair number two. Scenarios we've taken one of the six people to Now for each of those six scenarios, how many people, how many different people could sit in chair number two? Well each of those six There are six people whoĬould be in chair number one. We put in chair number one? Well there's six different And we can say look if no one's sat- If we haven't seated anyone yet, how many different people could Permutations of putting six different people into three chairs? Well, like we've seen before, we can start with the first chair. But it'll be very instructive as we move into a new concept. This is covered in the permutations video. ![]() One, chair number two and chair number three. Out all the scenarios, all the possibilities,Īll the permutations, all the ways that we could Video, we're going to say oh we want to figure Person B, we have person C, person D, person E, and we have person F. Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance.About different ways to sit multiple people in The number of ways of choosing 6 numbers from 49 is 49C 6 = 13 983 816. What is the probability of winning the National Lottery? You win if the 6 balls you pick match the six balls selected by the machine. In the National Lottery, 6 numbers are chosen from 49. The above facts can be used to help solve problems in probability. ![]() There are therefore 720 different ways of picking the top three goals. Since the order is important, it is the permutation formula which we use. In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10. The number of ordered arrangements of r objects taken from n unlike objects is: How many different ways are there of selecting the three balls? There are 10 balls in a bag numbered from 1 to 10. The number of ways of selecting r objects from n unlike objects is: Therefore, the total number of ways is ½ (10-1)! = 181 440 How many different ways can they be seated?Īnti-clockwise and clockwise arrangements are the same. When clockwise and anti-clockwise arrangements are the same, the number of ways is ½ (n – 1)! The number of ways of arranging n unlike objects in a ring when clockwise and anticlockwise arrangements are different is (n – 1)! There are 3 S’s, 2 I’s and 3 T’s in this word, therefore, the number of ways of arranging the letters are: In how many ways can the letters in the word: STATISTICS be arranged? The number of ways of arranging n objects, of which p of one type are alike, q of a second type are alike, r of a third type are alike, etc is: The total number of possible arrangements is therefore 4 × 3 × 2 × 1 = 4! The third space can be filled by any of the 2 remaining letters and the final space must be filled by the one remaining letter. The second space can be filled by any of the remaining 3 letters. The first space can be filled by any one of the four letters. This is because there are four spaces to be filled: _, _, _, _ How many different ways can the letters P, Q, R, S be arranged? The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). This section covers permutations and combinations. ![]()
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