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you are ordering a hamburger and can get up to 8 toppings, but each topping can be only be used once. You tell the cashier to surprise you with the toppings you get what is the probability that you would get zero toppings? Express your answer as a fraction or a decimal number rounded to four places decimal places .

Respuesta :

When you order the burguer you might get 0 toppings, or one, or two and so on.

Zero toppings can be done by choosing the combination of zero of the 8 possible toppings, that is:

[tex]_8C_0=\frac{8!}{0!(8-0)!}=1[/tex]

only one way.

All possible combinations of toppings is the sum of all the terms of the form:

[tex]_8C_r[/tex]

where r is the number of toppins. This means that r goes from zero to 8. Then all possible combinations of toppings is:

[tex]\begin{gathered} _8C_0+_8C_1+_8C_2+_8C_3+_8C_4+_8C_5+_8C_6+_8C_7+_8C_8 \\ =1+8+28+56+70+56+28+8+1 \\ =256 \end{gathered}[/tex]

Therefore the probability of getting zero toppings is:

[tex]P=\frac{1}{256}[/tex]

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