Question

suppose you have 7 physics texts, 9 computer science texts, and 8 math texts. how many different ways can you select 3 of each to take with you on vacation? express the answer to the combination problem using combination notation ($_nc_k$) and numerically.
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physics computer science math
combination notation: $\square c\square\times\square c\square\times\square c\square$
value: $\square$

Explanation:

Step1: Use combination formula for Physics texts

The combination formula is \(_{n}C_{k}=\frac{n!}{k!(n - k)!}\). For Physics texts, \(n = 7\) and \(k=3\), so \(_{7}C_{3}\).

Step2: Use combination formula for Computer Science texts

For Computer Science texts, \(n = 9\) and \(k = 3\), so \(_{9}C_{3}\).

Step3: Use combination formula for Math texts

For Math texts, \(n = 8\) and \(k = 3\), so \(_{8}C_{3}\).

Step4: Calculate the numerical value

$$
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$$

Answer:

Combination Notation: \(_{7}C_{3}\times_{9}C_{3}\times_{8}C_{3}\)
Value: \(164640\)