Person 1 can order from 6 different choices
Person 2 can order from 5 different choices
Person 3 can order from 4 different choices
Person 4 can order from 3 different choices

total choices = 6*5*4*3 =360

Hence option E is correct
Hit Kudos if you liked it

\(6P_4 = 360\)

Answer must be (E) 360

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Question: how many possible combinations of meals could they order?
which means "In how many ways can they order?"

There are 4 people: say A, B, C, D
There are 6 meals: say M1, M2, ... M6

You have 6 meals and you have to choose 4 of them - this is a combination problem
Now, you have to distribute the 4 meals among the 4 people - this is permutation
A - M1, B - M2, C - M3, D - M4
is different from
A - M4, B - M2, C - M3, D - M1

A ordering M1 is different from A ordering M4 and hence the 4 meals need to be arranged among A, B, C and D.

Had the question been: A person arrives at a restaurant to pick 4 meals to take home. He notices that the menu has 6 meal options. In how many ways can he pick the 4 meals?

Here, this is just selection - a combination problem.
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total choices ; 6*5*4*3 ; 360
IMO E
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