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Math Help - Combinations - Pizza Toppings

  1. #1
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    Combinations - Pizza Toppings

    I am just wondering if I did these questions correctly as I do not have an answer key for them.

    A second opinion would be greatly appreciated. Thanks.



    A pizza company has 15 toppings to choose from, of which 6 are vegetables.



    1. How many different three-topping pizzas have exactly one vegetable topping?

    = (all possible combinations of 1 veggie topping) x (all possible combinations of 2 non-veggie toppings)

    = _{6} C _1 x _{9} C _2

    = 216



    2. How many different three-topping pizzas have at least one vegetable topping?

    = (all possible combinations of 3-topping pizzas) - (pizzas without any veggies)

    = _{15} C _3 - _{9} C _3

    = 371



    3. How many different three-topping pizzas have exactly two vegetable toppings?

    = (all possible combinations of 2 veggie toppings) x (all possible combinations of 1 non-veggie topping)

    = _{6} C _2 x _{9} C _1

    = 135



    4. How many different three-topping pizzas have at least two vegetable toppings?

    = (all possible combinations of 3-topping pizzas) - (pizzas without any veggies) - (pizzas with exactly 1 veggie)

    = _{15} C _3 - _{9} C _3 - ( _{6} C _1 x _{9} C _2 )

    = 455 - 84 - 216

    = 155


    OR

    = (pizzas with exactly 2 veggies) + (pizzas with exactly 3 toppings)

    = ( _{6} C _2 x _{9} C _1 ) + _{6} C _3

    = 135 + 20

    = 155
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  2. #2
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    Grandad's Avatar
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    Hello Some_One

    You're doing a great job! I agree with all your answers.

    Grandad
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