If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 26 large cakes are needed for the party so \( \frac{26}{16} \) = 1\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 190 small cakes are needed for the party so \( \frac{190}{68} \) = 2\(\frac{27}{34}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 3 = 5 cooks.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)

1

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{94}{10} \) = 9\(\frac{2}{5}\)

So, it will take 9 full vans and one partially full van to transport the entire team making a total of 10 vans.