Questions about Counting Techniques ( Questions 11 - 14 ) 11. A pizzeria offers

Question

Questions about Counting Techniques (Questions 11 - 14)

11. A pizzeria offers the following choices for single-topping pizzas.
Sizes: 10”, 14”, 18”
Crust: Thin, Medium, Thick
Toppings: Sausage, Pepperoni, Mushrooms, Green Peppers

How many different types of pizzas are available?

12. How many distinct ways are there to arrange the letters of the word “Miami”? (Note:
Assume capital M and lowercase m are the same letter)

13. A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3
different heating systems, a garage or carport, and a patio or screened porch. How many
different plans are available to this buyer? (3 points)

14. A DNA sequence consists of a series of letters representing a DNA strand that spells out
the genetic code. There are 4 possible letters (A, C, G, and T), each representing a specific
nucleotide base in the DNA strand (adenine, cytosine, guanine, and Thymine,
respectively). How many distinguishable sequences can be found using two As, two Cs,
three Gs, and one T? In order to receive full credit, you must show all work in addition to
providing the correct answer.

Explanation / Answer

11) total number of type of pizzas =type of sizes*type of crusts*trype of toppings=3*3*4=36

12)there are 2 M, 2 i's and 1 a in Miami

hence number of arrangements =5!/(2!*2!*1!) =30

13)total plans =design choice*heating system choice*parking choice*patio choice =4*3*2*2=48

14)total number of ways =8!/(2!*2!*3!*1!)=1680

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