To find the number of different samples of 3 items that can be extracted from a batch of 10 items without replacement, you can use the combination formula ( C(n, r) = \frac{n!}{r!(n-r)!} ). Here, ( n = 10 ) and ( r = 3 ). Thus, the number of different samples is ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, you can extract 120 different samples.
Because with replacement, the total number of possible outcomes - the denominator of the probability ratio - remains the same. Without replacement the number of possible outcomes becomes smaller.
Not necessarily. A random sample can occur with or without replacement, depending on what makes more sense. For instance, trying to calculate the odds of a dice roll would require a random sample with replacement (because it is perfectly possible to get a 6 on each and every die); trying to calculate the odds of a poker hand, however, would require random sampling without replacement (the ace of spades can only show up once in any given round of dealing). when the population size is large enough, the difference between the two is meaningless; people who make national surveys, for instance, usually choose people randomly without replacement (there's no possibility they will survey the same person twice) but treat it as though the were sampling with replacement (because the math is easier). The only requirement for a random sample is that each object that might be chosen has a known and well-defined probability of being chosen at any given moment. For random samples with replacement that probability is always the same; For random samples without replacement that probability is determined by the objects that have previously been selected.
Different samples of a compound do not have different properties.
You don't need administrative rights to extract an archive.
Of course it is. The first draw always has 10 possibilities. The difference comes in the second draw. The second draw has 10 possibilities if the first one was replaced, but only 9 possibilities if the first one wasn't replaced.
Impossible without chromo.
I'm assuming vainla excart is vanilla extract. since the vanilla extract is only a flavoring agent, You can safely omit it, however the cookies will taste different. You can substitute have another extract (like almond!), but I would probably only use half the amount called for in the recipe.
two samples are independent if they are drawn from two different populations, and/ or the samples have no effect on each other. eg: We want to estimate the difference between the mean salaries of all male and all female executives. We draw one sample from the population of male executives and another from the population of female executives. These two samples are independent because they come from different populations and the samples have no effect on each other
No difference in the replacement procedure.
By using movable frames.
completely useless.
As a noun: I always use pure vanilla extract, never imitation vanilla flavoring.As a verb: They could not extract him from the wreck without cutting the car away with a 'jaws of life'.