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Five friends go to their favourite restaurant which has 8 different lunches on the menu. If the friends are equally likely to pick any of the dinners, what is the probability that two or more of the friends will order the same lunch?

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To find the probability that two or more of the friends will order the same lunch, you can use the complement probability, which is the probability that no two friends order the same lunch and subtract it from 1.

The first friend can choose from any of the 8 different lunches. The second friend, to avoid ordering the same lunch, has 7 choices. The third friend has 6 choices, the fourth friend has 5 choices, and the fifth friend has 4 choices.

So, the probability that no two friends order the same lunch is:

\(P(\text{No two friends order the same lunch}) = \frac{8}{8} \times \frac{7}{8} \times \frac{6}{8} \times \frac{5}{8} \times \frac{4}{8} \)

Now, calculate it:

\(P(\text{No two friends order the same lunch}) = \frac{7}{28} = \frac{1}{4}\)

Now, to find the probability that two or more of the friends will order the same lunch, subtract this from 1:

\(P(\text{Two or more friends order the same lunch}) = 1 - \frac{1}{4} = \frac{3}{4}\)

So, the probability that two or more of the friends will order the same lunch is \( \frac{3}{4} \) or 75%.
User Ali Sufyan
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