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A task-force is being formed for the TBRHSC, and the candidates include 13 senior staff members from emerge: How many different ways can we select 4 staff members t...

Question

A task-force is being formed for the TBRHSC, and the candidates include 13 senior staff members from emerge: How many different ways can we select 4 staff members to be on the task-force?Your Answer:AnswerQuestion 2 (1 point) Suppose that 3 of these staff members are doctors; and 10 of them are nurses. How many different ways can we select the task-force so that all 4 staff members are nurses?Your Answer:AnswerQuestion 3 (1 point) If the task-force is chosen randomly; compute the probability tha

A task-force is being formed for the TBRHSC, and the candidates include 13 senior staff members from emerge: How many different ways can we select 4 staff members to be on the task-force? Your Answer: Answer Question 2 (1 point) Suppose that 3 of these staff members are doctors; and 10 of them are nurses. How many different ways can we select the task-force so that all 4 staff members are nurses? Your Answer: Answer Question 3 (1 point) If the task-force is chosen randomly; compute the probability that all 4 staff members chosen will be nurses. Enter your answer as a decimal rounded t0 3 places; Your Answer:



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In Exercises 17–24, decide whether each exercise involves permutations or combinations, and then solve the problem.
A group of 3 students is to be selected from a group of 14 students to take part in a class in cell biology.
a. In how many ways can this be done?
b. In how many ways can the group who will not take part be chosen?

Okay. Today's question is how many ways can advise her Choose four students from a class of 12 if they're all assigned the same task. So we are going to use combinations to answer this question because the order does not matter, um, in this question, because they're all doing the same test. So we're going to do 12 or choosing out of 12 and we're picking four of them. So we use our combination formula, which is gonna be 12 fact Toro over four fact or oh, 12 minus four factorial. So once we simplify that, we have 12 facto room over four. Fact Toro eight. Fact Toro. Now what I would do to simplify is since 12 factorial means 12 times 11 times 10 and so on an eight factory means eight times seven times six and so on. We can cancel everything out, Um, from the eight and down. So that leaves us with on the top 12 times 11 times 10 times nine. And then the rest of that cancels out on the bottom. Since I canceled out the eight fact or oh, I still have the four factorial, which is four times three times two times one. Now I multiply that I get 11 8 80 I'm a top and 24 on the bottom, which will divide to give me 4 95 So there's 495 ways of choosing those four students. The second question as Hominy can students could be chosen if they're all given a different task. So now I'm going to use permutations because the order does matter. So I'm gonna do 12 p for instead of 12. C four and the formula for permutations will be 12. Fact, Toro over 12 minus four Fact. Toro. So I get 12 fact Toro over eight fact or oh, and again, just like on the last one, that all the way up to a it's gonna cancel. So I'm just gonna have 12 times, 11 times 10 times nine, which gives me the 11,880. So there's 11,880 ways to pick those four students if they're doing different

Let's try looking at this problem. The Digital Petro Company was recently successfully funded by a Kickstarter and must know and must now appointed president, chief executive officer, chief operating officer and the chief financial officer. It must also appoint a strategic planning committee with four different members. There are 10 qualified candidates, and the officers can also and officers can also serve on the committee. How many different ways can the four officers be appointed? Okay, so there is a committee off four different members and there are 10 qualified candidates and the officers can also serve on the committee. Okay, So since the since for the committee we have to select four members out of 10 we don't have to assign them any posts. Hence, using the combinations rule, we can write that the number off ways to form the committee, the number of ways to form the committee is then C four. Oh, this is nothing but 210 if I'm not wrong. Yes, do 10 How many different ways can the food officers we appointed and, uh, okay, this is the answer for second one. Actually, this is the answer for B. What is the answer for eight. And how many different ways can four officers were appointed? Well, 10 C four again, we are. We're selecting. We are selecting four officers from 10 again. This is 210 24. What is the probability that randomly selecting a committee member and getting four youngest off qualified candidates? What is the probability of selecting the committee members and getting four youngest off the qualified candidates? All right, so how many different ways are there in order to select a committee? 210 different ways. And there is only one possible selection in which will have four youngest of them. So this is going to be one divided by 210 This is going to be my probability. When divided by 210 This is a probability. Is there anything else? No. We have sold all the questions. This is my seat.

In how many different ways can the four officers were appointed? What are the different ways of selecting for people it is Tennessee for Or that I can see that. But now I also want toe arrange them in these four different office ing Sorry in these four different posts. So this is nothing but full factorial what I can say After finding the value of 24 which is to 10 I have to multiply it by four. Factory in. And what is this value turnout? This value turns out to be just a moment. I'll need a calculator for this. What does this well you turn out to be? That's what turns out to be 5040 This well is 50 405040 The next one says in How many possible ways can we select a committee? Simple. 10 c four were just selecting four people out of 10 or it does not matter. The posts don't matter. So it is 210 And the last part says, what is the probability of selecting the four youngest of them? Okay, there is only one possible combination off four youngest and the total number of possibilities are one divided by and the total number of possibilities are 210. So my probabilities wonderful about 210

All right. So amusing does most online scientific calculator, and I'm trying to get these three delegates. One of them has to be a professor. So if we have three professors and we have just one, that means that the other two have to come from the remaining five. That gives me 30 choices. If there are two professors on list, that means that the other, uh, plastic comb so can you. That and then there's always the choice of if all three are. And so, if I add 30 plus 15 plus one, there are 46 ways that we could choose his delegation.


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