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Thread: Counting and Probability

  1. #1
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    Counting and Probability

    Suppose You are ordering two pizzas.A pizza can be small,medium,large or extra large,with any combination of 8 possible toppings( getting no toppings is allowed, as is getting all 8) How many possibilities are there for your two pizzas?

    Answer: My answer is $\binom{4}{2}+\binom{4}{2}*2*(8+28+56+70+56+28+8+1 )=3066$ possibilities are there for ordering my two pizzas.
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  2. #2
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    Re: Counting and Probability

    You can get 4 sizes.

    You can get 0 to 8 toppings . This can be considered an 8 bit field. 1 for the topping is included, 0 for it's not.
    This is $2^8=256$ different topping combos.

    So for a single pizza there are $4 \cdot 256 = 1024$ different combinations.

    Thus for two pizzas there are $1024^2 = 1,048,576$ different two pizza combos.
    Thanks from Vinod
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  3. #3
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    Re: Counting and Probability

    Quote Originally Posted by romsek View Post
    You can get 4 sizes.

    You can get 0 to 8 toppings . This can be considered an 8 bit field. 1 for the topping is included, 0 for it's not.
    This is $2^8=256$ different topping combos.

    So for a single pizza there are $4 \cdot 256 = 1024$ different combinations.

    Thus for two pizzas there are $1024^2 = 1,048,576$ different two pizza combos.
    Hello,
    Your answer looks correct.
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