Bissoy.com
Doctors Medicines MCQs Q&A

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors? Correct Answer None of these

Required number of ways
$$ = \left( {{}^4{C_4} \times {}^6{C_1}} \right) + $$   $$\left( {{}^3{C_3} \times {}^4{C_{2}}} \right)$$
$$\eqalign{ & = \left( {1 \times 6} \right) + \left( {1 \times \frac{{4 \times 3}}{2}} \right) \cr & = \left( {6 + 6} \right) \cr & = 12 \cr} $$

Related Questions

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done if the committee should have 2 trainees and 2 research associates?
A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associate. In how many different ways can this be done if the committee should have 2 trainees and 3 research associates?
Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees-K1, K2 and K3, and each candidate should serve on exactly one of the committees. Committee K1 should consist of exactly one member more than committee K2. It is possible that there are no members in committee K3. Among Z, Y and X none can serve on committee 10. Among W, V and U none can serve on committee K2. Among T, S and R none can serve on committee K3. In case committee K2 is served by T and Z only, how many of the nine individuals should serve on committee K3?  Of the nine individuals, the largest number that can serve together on committee K3 is:
Two statements are followed by two Conclusions I and II. You have to consider the statements to be true, even if they seem to be at variance from commonly known facts. You are to decide which of the given conclusions can definitely be drawn from the given statements and indicate your answer accordingly. Statements: I. The Enforcement Directorate (ED) has sought information on offshore investments by directors of RNT Associates, a closely held firm which functions as a family office and investment vehicle of Ratan Tata.  II. The ED order, dated June 14, also calls for details of investments or loans from RNT Associates and its directors to a Singapore-based entity, RNT Associates Ltd. Conclusions: The order is under provisions of the Foreign Exchange Management Act (FEMA) and the documents are being sought for the purpose of investigation under FEMA. The nature of queries from Enforcement Directorate is related to RNT Associates’ investment portfolio. It is compliant with all disclosures and existing laws governing investments and is extending all cooperation.
Nine individuals - Z, Y, X, W, V, U, T, S and R - are the only candidates, who can serve on three committees-K1, K2 and K3, and each candidate should serve on exactly one of the committees. Committee K1 should consist of exactly one member more than committee K2. It is possible that there are no members in committee K3. Among Z, Y and X none can serve on committee 10. Among W, V and U none can serve on committee K2. Among T, S and R none can serve on committee K3. In case committee K2 is served by T and Z only, how many of the nine individuals should serve on committee K3? 
In a sample of associates at a low firm. 30 percent are second -year associates, and 60 percent are not first-year associates . That percentage of the associates at the law firm have been there for more than two years?
In a sample of associates at a law firm, 35 percent are second yer associates, and 55 percent are not first -year associates. That percentage of the associates at he law firm have been there for more than two years?
In a sample of associates at a law firm, 35 percent are second year associates, and 55 percent are not first-year associates. That percentage of the associates at the law firm have been there for more than two years?
24 experts can do as much work as 40 trainees in a given period of time. A piece of work can be done by 9 experts and 25 trainees. How many trainees alongside 12 experts would one need to complete a similar work in the same duration of time?
The question below consists of a set of labelled sentences. Out of the four options given, select the most logical order of the sentences to form a coherent paragraph. P: Inclusion is also about finding different ways of teaching so that classrooms actively involve all children. It also means finding ways to develop friendships, relationships and mutual respect between all children, and between children and teachers in the school. Q: Creativity may mean teachers learning to teach in different ways or designing their lessons so that all children can be involved. R: Inclusive education is about looking at the ways our schools, classrooms, programs and lessons are designed so that all children can participate and learn. S: All children are at all times ready to attend regular schools and classrooms. Their participation is not something that must be earned. Inclusive education is a way of thinking about how to be creative to make our schools a place where all children can participate.