Students at a Private Liberal Arts College Are Classified
Students at a private liberal arts college are classified as existence freshmen, sophomores, juniors, or seniors, and also according to whether they are male or female person. Notice the total number of possible classifications for the students of that college.
Students at a private liberal arts higher are classified as beingness freshmen, sophomores, juniors, or seniors, and also according to whether they are male or female. Detect the total number of possible classifications for the students of that college.
Students at a individual liberal arts college are classified as being freshmen, sophomores, juniors, or seniors, and besides according to whether they are male person or female. Detect the total number of possible classifications for the students of that college.
When solving for possible classifications and outcomes, yous will need to determine the number of categories that you have. In this case, nosotros have four categories. We have majors. We have miners, we have twelvemonth of student and we have the gender of the educatee. These four categories determine the number of classifications. The number of majors at this academy or, um, studies are as 32 different studies and yous can't minor in a major. So in one case you've major in it, yous've lost the ability to pocket-size in that major. And then there really is only 31 miners left, just we volition. We will use the number 32 besides in this example because in that location is the pick of not monitoring at all. And so you accept 31 possible miners, only then one more as a not minor. So 32 total options In that location are four options for years, and there are two options for genders. And so to exercise the counting principal, you will multiply the outcomes of each category 32 times, 32 times iv times ii. And the respond in this case would equal 8000 100 92. That would be 8100 in 92 possible classifications for students
Then in this problem, we are considering how many different student classifications are there. And we have different criteria. They're gonna help u.s.a. observe out the possible different classifications in this problem. At that place is, um, a choice of major a option of minor, a year of the educatee and a gender. And so we consider these 4 categories to find out the total number of classifications. So for the first, um, topic first, Ah, subject there is what nosotros call a major. I'll depict a line hither and put an Grand a below information technology for Major. Now there are 32 different majors, so there are 32 possible possible classifications. Ah, the next item would exist a pocket-sized. Now you lot would recollect, Well, let'due south run into here There'south 32 miners, but you lot would be wrong because there are actually only 31 miners. You can't pocket-sized in a major. So, um, once you lot major in a subject, that subject is then removed and you only have 31 more possible choices to pick for a minor. Now. Actually, y'all'd be right with y'all, said 32 merely accidentally probably because even though there are only 31 miners to option from. Nosotros at present have the pick of not picking a minor. Y'all can major in. Ah, non small-scale and something. At present you can't small and not major. Some things that would be possible. And then with a major, there are 32 majors with a minor. There are 31 miners, but them with the non modest idea are possibility. There are actually 32 different ways. You couldn't small-scale 31 miners plus one no minor. So we'll put a 31 32 in a higher place the minor. At present in that location are two more than categories. 1 is the year of the educatee will put twelvemonth. Why for yr here and there are 4244 years, starting time year, second year, third year and fourth twelvemonth In the last category is the gender or the sex activity. Then put s for sex and you have two dissimilar sexes male and female person. So these are your categories in the outcomes of each of those categories and using the cardinal counting principle, we was just multiply these categories together to get our answer. Now our answer. If y'all multiply these together with the 8000 100 92 8000 192 and this is this number 80,192 is the different the full unlike pupil classifications that are possible 8192 of them.
He has articulate. So when y'all're in here, so nosotros're gonna utilize the pigeonhole principle with the student suspicions. And then there are four times 21 different pigeonholes, which gives us 84 since the holes are pairs of both graduate ear and major. So we're gonna find a positive integer cease for which this holds to be true. Then we meet that and has to be equal to beauty four times two minus i plus one, which is 85 students.
A problem. fourteen 7. Nosotros accept six 1000000 and for a woman. And then nosotros are given that 60 off to. So we have to choose to men and two women. Um, through the number of ways to a select two men and 2 women. Choosing from 6 from half-dozen men is, uh, 4 C two. So the number of ways to women can be chosen from 4 is six seed to times for C 2, which is equal to, uh, which is able tonight. Eso the number off means to men and 2 women can be chosen is 90 in 19 weeks.
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signal) Notation: When using interval note in WeBWorK , remember that: You employ 'INF' for 0 and '-INF' for And employ 'U' for the union symbol; Enter DNE if an answer does not exist, flz) = 4sin x COS I, on (-T,T) a) Determine the intervals on which is concave upwards and concave...
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