Manny's burrito stand lets customers choose 4 ingredients from the list below to add their burritos:
\begin{tabular}{|c|c|c|c|}
\hline Onions & Cilantro & Jalapeño & Beans \
\hline Cheese & Crema & Salsa & Hot sauce \
\hline
\end{tabular}

How many groups of 4 different ingredients can go on a burrito?

Question

Manny's burrito stand lets customers choose 4 ingredients from the list below to add their burritos:
\begin{tabular}{|c|c|c|c|}
\hline Onions & Cilantro & Jalapeño & Beans \
\hline Cheese & Crema & Salsa & Hot sauce \
\hline
\end{tabular}

How many groups of 4 different ingredients can go on a burrito?

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the number of different groups of 4 ingredients that can be chosen from 8 ingredients, we use the binomial coefficient. ‖ ‖ step 2 ⋮ The binomial coefficient formula is $\binom{n}{k} = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items, and $k$ is the number of items to choose. ‖ ‖ step 3 ⋮ Applying the formula with $n=8$ and $k=4$, we get $\binom{8}{4} = \frac{8!}{4!(8-4)!}$. ‖ ‖ step 4 ⋮ Simplifying the expression, we have $\binom{8}{4} = \frac{8!}{4!4!} = \frac{8 imes 7 imes 6 imes 5}{4 imes 3 imes 2 imes 1}$. ‖ ‖ step 5 ⋮ Calculating the simplified expression gives us $\binom{8}{4} = 70$. ‖ ∻Answer∻ ⚹ There are 70 different groups of 4 ingredients that can go on a burrito. ⚹ ∻Key Concept∻ ⚹Combinations and the Binomial Coefficient⚹ ∻Explanation∻ ⚹The number of ways to choose $k$ items from a set of $n$ distinct items is given by the binomial coefficient $\binom{n}{k}$, which is calculated using the formula $\binom{n}{k} = \frac{n!}{k!(n-k)!}$. This represents the number of combinations possible without regard to order.◊What is the formula to calculate the number of combinations of ingredients for Manny's burrito stand?⍭ Generate me a similar question◊⚹

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