**Q1. 5 children are to be seated on a bench. In how many ways can it be done if the eldest child always sits in the middle?**

(a) 48

(b) 12

(c) 36

(d) 24

**Q2. Find the number of ways in which 8 players out of 12 players can be selected such that 2 particular players are always included and 3 particular players are always excluded?**

(a) 6

(b) 7

(c) 8

(d) 9

(e) None of these

**Directions (Q3-5): Read the following information and answer the questions given below it.**

**A committee of 7 members has to be formed from 9 men and 4 women. In how many ways can this be done when the committee consists of**

**Q3. Exactly 3 women?**

(a) 504

(b) 505

(c) 506

(d) 507

(e) None of these

**Q4. Atleast 3 women?**

(a) 586

(b) 587

(c) 588

(d) 589

(e) None of these

**Q5. At the most 3 women?**

(a) 1634

(b) 1633

(c) 1632

(d) 1631

(e) None of these

**Q6. The probability that a leap year selected at random contains 53 Sundays, is**

(a) 7/366

(b) 26/183

(c) 1/7

(d) 2/7

(e) 4/11

**Q7. Let E be the set of all integers with 1 at their unit places. The probability that a number chosen from {2, 3, 4, ………. , 50} is an element of E, is**

(a) 5/49

(b) 4/49

(c) 3/49

(d) 2/49

(e) 10/13

**Q8. A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red?**

(a) 1

(b) 1/7

(c) 3/14

(d) 3/28

(e) None of these

**Q9. Two persons A and B appear in an interview for two vacancies. If the probabilities of their selections are 1/4 and 1/6, respectively, then the probability that none of them is selected is**

(a) 5/8

(b) 5/12

(c) 1/12

(d) 1/24

(e) None of these

**Q10. In a ward-robe, Nitish has 3 trousers. One of them is black, second is blue and third brown. In this ward-robe, he has 4 shirts also. One of them is black and the other 3 are white. He opens his ward-robe in the dark and picks out one shirt-trouser pair without examining the colour. What is the likelihood that neither the shirts nor the trousers are black?**

(a) 1/12

(b) 1/6

(c) 1/4

(d)1/5