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Answer :
There are 2,520 different ways to arrange 5 out of the 9 fancy cakes in a row for a bakery display, as calculated using permutations without repetition.
The number of ways to line up 5 out of 9 fancy cakes in a row for a bakery display, which is a problem of permutations without repetition.
To solve this, one would use the permutation formula which is P(n, k) = n! / (n - k)!.
Where 'n' is the total number of items to choose from (in this case, 9 cakes), and 'k' is the number of items to arrange (in this case, 5 cakes).
So we calculate P(9, 5) = 9! / (9 - 5)! = 9 x 8 x 7 x 6 x 5 / 4!. The 4! (which is 4 x 3 x 2 x 1) in the denominator cancels out the 6 x 4, simplifying the calculation to 9 x 8 x 7 x 5 = 2,520.
Therefore, there are 2,520 different ways to arrange 5 out of the 9 fancy cakes in a row.
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