II. Solve the following problems. Show all pertinent solutions. 1. Evaluate the value of the following expressions: (a) Co+C1 +C2 +C3 +C4 (b) 7C3 + 7C4+ 7Cs +7C6 +7C7 (c) 2 (sP3-C2) 6 (sP3 P3)-5 (sCa*6C3) (d) 2. How many different committees of 4 members can be formed from a group. with 7 seniors and 6 juniors? 3. How many different committees with 4 members can be formed from a group with 7 seniors and 6 juniors if (a) they are all seniors? (b) there are 3 seniors and 1 junior? (c) there are equal number of seniors and juniors in each committee? 4. A class consists of 12 boys and 10 girls. In how many ways can a committee of five be formed if (a) all the members are boys? (b) 2 are boys and 3 are girls? 5. A box contains 2 red, 5 blue, and 5 yellow balls. In how ways can 3 balls be drawn from the box? 6. A box contains 2 red, 5 blue, and 5 yellow balls. In how many ways can three balls be drawn from the box such that (a) they are all blue? (b) there no blue balls? (c) 2 are red and 1 is yellow? (d) they are of different colors? 7. In how many ways can a student answer an exam if out of the 6 problems, he is required to answer only five? 8. In a given examination, a student is required to answer 5 of the 7 questions including 3 of the first 4 questions. In how many ways can he answer the examination?

1.If the volume of a box is represented by the expression (x3 - 3x2 -10x + 24) cm3 and the width is (x - 2) cm. What are the other dimensions? A. (x + 3) (x - 4) B. (x - 3) (x - 4) C. (x - 3) (x + 4) D. (x + 3) (x + 4) 2.One of the roots of -5x2(x3 + 2x - 7) is 0. How many other roots are there? A. 3 B. 4 C. 5 D. 6 3.Which polynomial equation has 1, -2, and 3 as roots? A. P(x) = (x + 1) (x – 2) (x + 3) B. P(x) = (x – 1) (x + 2) (x – 3) C. 2 (x + 1) (x + 2) (x + 3) D. 2 (x - 1) (x - 2) (x - 3) 4.Which of the following polynomial equations has 2 as one of the roots? A. x2 – 5x + 8 = 0 B. 4x3 – 9x2 - 3x = 0 C. 4x4 + 8x3 - 39x2 = 0 D. x3 + 6x2 – 16x = 0 5.The polynomial equation whose roots are {-1, - ½ and 3} is _______ A. 2x3 – 3x2 – 8x – 3 = 0 B. x3 - 6x2 – x – 3 = 0 C. 2x3 + 3x2 – 5x – 3 = 0 D. 2x3 + 3x2 + x – 15 = 0

C. Remove all grouping symbols and simplify 13. 2x-[(3y + 5x) - (8x-6y)] 14. 4a²-5(a + 3b)-[2(a² + 5b-7a) -(6a-4b)] 15. 6(3x + 4y-52)-2[(7x-8y+z) - 9y + 5y] 16. 5[(3a-4b+c)-(2a-6c)]-4(7a-b-3c) 17. 8y-(3y + 4y-7)-[2(7y² + 6y-9) - (y²-8y + 10)]

Which of the following is equivalent to (3x - 8)(3x - 2)? O 9x2- 18x+16 9x² + 18x - 16 O9x2-30x - 16 9x2-30x + 16