ExplanationYou are forming groups where order doesn’t matter, so use the combination formula.

If you use 5 ingredients, then there are: \(\frac{10}{5}\times\frac{9}{4}\times\frac{8}{3}\times\frac{7}{2}\times\frac{6}{1}=252\) different combinations.

If you use 6 ingredients there are \(\frac{10}{6}\times\frac{9}{5}\times\frac{8}{4}\times\frac{7}{3}\times\frac{6}{2}\times\frac{5}{1}=210\) combinations, if you use 7 there are \(\frac{10}{7}\times\frac{9}{6}\times\frac{8}{5}\times\frac{7}{4}\times\frac{6}{3}\times\frac{5}{2}\times\frac{4}{1}=120\), and if you use 8 there are \(\frac{10}{8}\times\frac{9}{7}\times\frac{8}{6}\times\frac{7}{5}\times\frac{6}{4}\times\frac{5}{3}\times\frac{4}{2}\times\frac{3}{1}=45\).

Thus, Quantity A is 8, and Quantity B is 5, choice A.
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Sandy

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