Question

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?)

Answer 1

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

let us solve using combination,

`^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=`

we know that,

`^nC_0+^nC_1+^nC_2+\ldots+^nC_5=2^n`

thus,

`\begin{gathered} ^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=2^5 \\ =32 \end{gathered}`

hence, there are 32 ways to pick the toppings.