By taking in mind the number of combinations of 4 out of the 7 dishes, and the possible orders of these 4 dishes, we will find that there are 840 unique ways to arrange 4 of the 7 dishes.
We know that if we have a set of N elements, the total number of different combinations of K elements (K ≤ N) out of the N elements is given by:
In this particular case, we have:
- N = number of available dishes = 7
- K = number that we need to select = 4
Then the number of different combinations is given by:
Now we have 4 dishes selected, but we also need to order them.
- For the first dish, there are 4 options.
- For the second, there are 3 options (as one was already selected).
- For the third, there are 2 options.
- For the last one there is only one option.
The number of different arrangements of the dishes is given by the product between the numbers of options above, this gives:
4*3*2*1 = 24
Then the total number of unique ways of arranging 4 of the 7 dishes is:
C = 24*35 = 840
Where we take in mind the possible number of combinations of 4 out of the 7 dishes, and the possible orders of these 4 dishes.
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