91Ó°ÊÓ

Express each row of Pascal's triangle using combinations. Leave each term in the form \(_{n} C_{r}\). a) \(1 \quad 2 \quad 1\) b) \(1 \quad 4 \quad 6 \quad 4 \quad 1\) c) \(1 \quad 7 \quad 21 \quad 35 \quad 35 \quad 21 \quad 7 \quad 1\)

In how many different ways can you arrange all of the letters of each word? a) hoodie b) decided c) aqilluqqaaq d) deeded e) puppy f) baguette

Use the binomial theorem to expand. a) \((x+y)^{2}\) b) \((a+1)^{3}\) c) \((1-p)^{4}\)

Four students are running in an election for class representative on the student council. In how many different ways can the four names be listed on the ballot?

Explain how Pascal's triangle is constructed.

Describe the cases you could use to solve each problem. Do not solve. a) How many 3 -digit even numbers greater than 200 can you make using the digits \(1,2,3,4,\) and \(5 ?\) b) How many four-letter arrangements beginning with either B or E and ending with a vowel can you make using the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{E}, \mathrm{U},\) and \(\mathrm{G} ?\)

a) Determine the sum of the numbers in each of the first five rows in Pascal's triangle. b) What is an expression for the sum of the numbers in the ninth row of Pascal's triangle? c) What is a formula for the sum of the numbers in the \(n\) th row?

In how many ways can four girls and two boys be arranged in a row if a) the boys are on each end of the row? b) the boys must be together? c) the boys must be together in the middle of the row?

How many six-letter arrangements can you make using all of the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and \(\mathrm{F}\), without repetition? Of these, how many begin and end with a consonant?

Iblauk lives in Baker Lake, Nunavut. She makes oven mitts to sell. She has wool duffel in red, dark blue, green, light blue, and yellow for the body of each mitt. She has material for the wrist edge in dark green, pink, royal blue, and red. How many different colour combinations of mitts can Iblauk make?