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At a restaurant, the choices for hamburger toppings are cheese, tomato, lettuce,onion, mayo, mustard, ketchup and pickles. If you choose 5 toppings, how manyways can you pick your toppings?(Hint: Is this a combination or permutation?)

Respuesta :

at the restauant we can choose 5 topping for a hamburger,

let us solve using combination,

[tex]^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=[/tex]

we know that,

[tex]^nC_0+^nC_1+^nC_2+\ldots+^nC_5=2^n[/tex]

thus,

[tex]\begin{gathered} ^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=2^5 \\ =32 \end{gathered}[/tex]

hence, there are 32 ways to pick the toppings.

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