In a cafeteria, there are 5 breads. One can choose 1 bread from the available breads, either small or large sized, and can choose up to 2 sauces from 6 available sauces. What is the number of different ways one can place an order?

Question

The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a$, $b$, $c$, and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d)$ is ?

Answer 1

Step 1: Number of bread options: each of the $5$ breads can be small or large, giving $5\times2=10$ choices.
Step 2: Number of sauce combinations, choosing up to $2$ from $6$: none $(1)$, exactly one $(6)$, or exactly two $\left(\binom{6}{2}=15\right)$, totaling $1+6+15=22$.
Step 3: Multiply the independent choices: \[ 10\times22=\boxed{220} \]

In a cafeteria, there are 5 breads. One can choose 1 bread from the available breads, either small or large sized, and can choose up to 2 sauces from 6 available sauces. What is the number of different ways one can place an order?

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Correct Answer: 220

Solution and Explanation

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