Question: 1. Simplify (4marks) (n+4)! (n+3) (n+2) (n+1) n! 2. How many different arrangements of letters can be made from the words: (6 marks) a) NIKKKILEE

a) NIKKKILEE b) SASKATCHEWAN 3. In a survey of grades from 400

first-year science students at a university, it was found that 55 students

got an A grade in mathematics, 65 got an A in physics,

1. Simplify (4marks) (n+4)! (n+3) (n+2) (n+1) n! 2. How many different arrangements of letters can be made from the words: (6 marks) a) NIKKKILEE b) SASKATCHEWAN 3. In a survey of grades from 400 first-year science students at a university, it was found that 55 students got an A grade in mathematics, 65 got an A in physics, 40 got an A in chemistry, 25 got an A in math and physics, 23 got an A in math and chemistry, 21 got an A in physics and chemistry, and 15 got an A in all three subjects. Assume that all 400 students took math, physics, and chemistry. a) Draw a Venn diagram to illustrate this situation. b) How many students did not get any A's? (6 marks) 4. The following arrangements of letters start at the top and then proceed to the next row by moving diagonally left or right. Determine the number of different paths that would spell the word PERMUTATION. Explain your steps using Pascal's method. ( 4 marks) P E E R RR MMMM U U U U U TTT TTT AAAAA TT TT III 0 0 N

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