5

(A) A TEACHER wishEs To Break KER CLAsS OF 20 STuDENt3 into 5 GRoups OF 4 DIFFEREUT StuDENTS _ Kow MANY DiFFEREUT WayS ARE THERE T0 Do t#is?...

Question

(A) A TEACHER wishEs To Break KER CLAsS OF 20 STuDENt3 into 5 GRoups OF 4 DIFFEREUT StuDENTS _ Kow MANY DiFFEREUT WayS ARE THERE T0 Do t#is?

(A) A TEACHER wishEs To Break KER CLAsS OF 20 STuDENt3 into 5 GRoups OF 4 DIFFEREUT StuDENTS _ Kow MANY DiFFEREUT WayS ARE THERE T0 Do t#is?



Answers

In
order
to conduct
an
experiment,
five
students
are
randomly selected
from
a
class
of $ 20 $.
How
many
different
groups of
five
students
are
possible?

Were asked to answer a question about forming an experimental group using county principles, we're told, in order to conduct an experiment that researchers randomly select five students in the class of 20 students and were asked how many different groups of five students are possible. Well, first of all, would be looking for Well, we're looking at at different groups of five students out of the 20 and we don't really care about the order in which the students are picked. So we're looking for number of combinations of 20 students taken five at a time. This is, of course, 20 C five, and this is equal to buy the Formula 20 factorial over 20 minus five. Factorial comes five factorial, which is 20 factorial over 15 factorial times five factorial, which is 20 times 19 times 18 times 17 times 16 over five times, four times three times, two times one. Now we can simplify this a little bit. Divide out the 54 and the 20 you can divide three and 18, 18 becomes a six. You can divide 16, so it becomes eight to so this reduces to 19 times six times 17 times eight, and he plugged this into a calculator. This is 15,000 504

So Would you find the number of groups of five soon as possible within the class? Um and there's a group of 20. So you can write that as 20 C5 which is equal Uh huh. For me. Mhm. For me Ones files. Oh, so that is going to be equal to for me 16. Yeah. So we can write like that as mm I was 19 18 times 17, 16 times 15 Over 15. We know this country as well, comes forecast. And then so we will end up getting Amount to 93,000, 90, over steps Equals 15504.

33. We are interested in the number of different ways in which we can select five out off 30 students. Eso Since the order is not important, we use a combination to calculate this possible away is which is 30 factorial over five factorial 30 minus five Victorians who is equal to 30 Victorian over five factorial times 25 factorial using calculators way get the results which is 14 to 5, five or six different ways toe form the five groups.

In this problem, we have four professors and six students And we have to make a committee of five To include at least two professors. So let us take case one in which we take two professors. So there are five seats, two professors are already taken. So there are remaining three seats for students. So out of those four professors we will choose to professors for two professors Multiplied by out of six students will choose three students Comes out as four and 2, three by two and two, six into 5 into 4. 5, six gets canceled, says to he says six and two 20 which is wondering now let us take case two In which we choose three professors and those students. This can be done using out of four professors will choose three professors and out of six students rituals to students. Four c three's four Into, 62,-, five, It's just 15 and 24, which is 60 to stake. History Enrich. Four professors are chosen and only wants to rent. Has chosen. This can be done in four c foot. I'm gonna ways to choose the professors into 61 just nothing but one and do six, which is six. So daughter movies. What number of choices so that we have at least two professors will be addition of case one. Case too. In case three, which is 1 20 plus 60 plus six inches 186. That's


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