Asha has 8 different storybooks. She wants to take 3 of them with her on a holiday. In how many ways can she choose the 3 books? (The order of choosing does not matter.)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 56
Choosing \(r\) things from \(n\) different things, when order does not matter, is a selection: \(^nC_r=\frac{n!}{r!\,(n-r)!}\).
Books \(n=8\), books chosen \(r=3\)
\(\displaystyle ^8C_3=\frac{8\times7\times6}{3\times2\times1}=\frac{336}{6}=56\)
Why the other options are incorrect
Option (2) 336 — Incorrect. This is \(^8P_3\), which counts the order of choosing; the order does not matter here.
Option (3) 24 — Incorrect. This is \(8\times3\), which is not a counting rule.
Option (4) 28 — Incorrect. This is \(^8C_2\), the count for choosing 2 books, not 3.