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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: hello_kitty on October 13, 2011, 08:48:30 pm

Title: Help with Combinatorics! :( Using mulitiplication and addition principle
Post by: hello_kitty on October 13, 2011, 08:48:30 pm

Hey guys i have 6 questions im getting confused on!

1) THe menu in a restaurant lists 4 choices of entrees, 8 mains, and 4 desserts. find the number of choices of meal possible for:
    If you can choose to omit the entree

Answer: 160

2) A particular new model of a car is available in 5 chioces of colour, 3 choices of transmission, 4 types of interior, and 2 types of engine. Air conditionining is optional. How many different types of car are possible?

Answer: 240


3) Morse code consists of a succession of dots and dashes. The symbols formed byt he code may consist of 1,2,3 or 4 dots or dashes. How many different symbols may be represented by this code?

Answer: 30

4) A game of mini Tatslotto consists of choosing 3 numbers from 1,2,3,4 and 5. How many are there?

Answer: 50

5) A magazine costs $5.60 and you will pay with $6. How manyw ays could you receive your change?

Answer: 40c can be given in 9 ways

6)In a fruit bowl are 3 bananas (1 lady finger, 1 green and 1 normal), 2 apples (1 green and 1 red), and 1 plum
You decide to pick another piece of fruit so you have 2 in total. How many are there?

Answer: 15

Thanks!!

Title: Re: Help with Combinatorics! :( Using mulitiplication and addition principle
Post by: yawho on October 13, 2011, 09:13:43 pm

(1)  5 choices of entrees (including no entree) x 8 x 4 =160

Title: Re: Help with Combinatorics! :( Using mulitiplication and addition principle
Post by: yawho on October 14, 2011, 08:05:48 pm

(2) 5 x 3 x 4 x 2 x 2 (with/without air) = 240

Title: Re: Help with Combinatorics! :( Using mulitiplication and addition principle
Post by: oldschool on October 15, 2011, 11:40:58 am

Q3:

combinations possible from 1 dot/dash:  2^1  (2 because there are 2 possibilities for each symbol, dot or dash)
"                                          2 dot/dash:  2^2
"                                          3 dot/dash:  2^3
"                                          4 dot/dash:  2^4

2^1 + 2^2 + 2^3 + 2^4 = 30

Title: Re: Help with Combinatorics! :( Using mulitiplication and addition principle
Post by: yawho on October 16, 2011, 07:07:06 am

(6) 6C2 = 15