**Directions (1-2): Study the following information carefully to answer the questions that follow.**

**A committee of five members is to be formed, out of 4 students, 3 teachers and 2 sports coaches. In how many ways can the committee be formed if,**

**Q1. The committee should consist of 2 students, 2 teachers and 1 sports coach?**

(a) 25

(b) 64

(c) 9

**(d) 36**

(e) None of these

**Q2. Any five people can be selected?**

**(a) 126**

(b) 45

(c) 120

(d) 24

**Directions (3-4): Study the given information carefully and answer the questions that follow.**

**A committee of five 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**

**Q3. The committee should have all 4 professors and 1 research associate or all 3 trainees and 2 professors?**

**(a) 12**

(b) 13

(c) 24

(d) 52

(e) None of these

**Q4. The committee should have 2 trainees and 3 research associates?**

(a) 15

(b) 45

**(c) 60**

(d) 9

(e) None of these

**Q5. A property tax increase was proposed by a municipal corporation and it was observed that 40% of the property owners favoured it while 80% of the non-owners of property favoured it. If 70% of voters are property owners, what is the probability that a voter selected at random would be the one favouring the tax increase?**

(a) 0.80

**(b) 0.52**

(c) 0.40

(d) Data inadequate

(e) None of these

**Q6. In how many different ways can be numbers ‘256974’ be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?**

**(a) 48**

(b) 720

(c) 36

(d) 360

(e) None of these

**Q7. On a shelf, there are 4 books on Economics, 3 books on Management and 4 books are Statistics. In how many different ways, can the books be arranged so that the books on Economics are kept together?**

**(a) 967680**

(b) 120960

(c) 5040

(d) 40320

(e) None of these

**Directions (8-10): Study the given information carefully to answer the questions that follow.**

**A committee of 6 teachers is to be formed out of 4 science teachers, 5 Arts teacher and 3 Commerce teacher. In how many different ways, can the committee be formed, if**

**Q8. Two teachers from each stream are to be included?**

(a) 210

**(b) 180**

(c) 145

(d) 96

(e) None of these

**Q9. No teacher from the Commerce stream is to be included?**

(a) 81

(b) 62

(c) 46

(d) 84

(e) None of these

**Q10. Any teacher can be included in the committee?**

(a) 626

(b) 718

**(c) 924**

(d) 844

(e) None of these

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MAHENDRA GURU