1. How many permutations of the letters of the word HEAVEN are there if the vowels are to be written together?

a)72

b)144

c)120

d)720

2. Ina certain group of 50 students at Hogwarts School of Wizardry, only 15 students are wearing caps and 30 students are wearing neckties. If 9 students are neither wearing a cap nor a necktie, how many students are wearing both cap and a necktie?

a)3

b)4

c)5

d)6

3. In how many way can 5 plus signs and 6 minus signs be written in a line?

a)86,400

b)2880

c)462

d)2418

4. In the Martian Language, any permutation of letters forms a word. How many 4 - letter Martian words can be formed from the letters Q, U, I and Z?

a)24

b)4

c)12

d)3

5. How many committees consisting of 1 boy and 1 girl can be selected from a group of 3 boys and 2 girls?

a)5

b)6

c)8

d)12

6. How many committees of 6 men each can be selected from 9 men if a certain 2 men refuse to serve together on any committee?

a)49

b)84

c)35

d)840

7. In how many relative orders can 7 people sit at a round table with a certain 3 people sitting side by side?

a)144

b)720

c)540

d)108

8. In the Pinoy Big Brother House, the original housemates composed of 6 males and 6 females were asked to form groups of 3 before they can perform their daily task. How many possible groups can the housemates form if the same sex stays together?

a)220

b)20

c)40

d)400

9. From the digits 0, 1, 2, 3, 4, and 5, how many 3-digit numbers can be formed if digits may be repeated but the first digit must not be zero?

a)100

b)159

c)120

d)180

10. Out of 6 statistician and 8 mathematician, a special task force is to be formed consisting of 3 statisticians and 4 mathematicians. In how many ways can this be done if 2 particular statisticians and a particular mathematician must be included in the task force?

a)1400

b)140

c)201 600

d)90

11. In how many ways can 3 men and 4 women be seated on a bench if the women are to be seated together?

a)720

b)220

c)1024

d)576

12. At a round table seating twelve, in how many relative orders can we seat 6 men and 6 women in alternate seats?

a)479,001,600

b)518,400

c)86,400

d)14,400

13. In how many ways can a hostess select 6 luncheon guests from 10 women if she is to avoid having a particular two of the women together at the luncheon?

a)210

b)140

c)70

d)151,200

14. In how many ways can 5 people line up to pay their electricity bills if two particular persons refuse to follow each other?

a)48

b)90

c)72

d)140

15. How many ways can a committee of 6 members be selected from an organization with 20 members?

a)38,760

b)21,520

c)23,450

d)32,015