What is the number of arrangements of 5 distinct books on a shelf if 2 particular books must always be adjacent?
Answer and explanation
Correct answer: D. 48
- Step 1: Tie the 2 particular books together as a single block. Now we have 4 units to arrange.
- Step 2: Number of ways to arrange 4 units is .
- Step 3: The 2 particular books can be arranged internally in ways.
- Step 4: Total arrangements: .
Answer
48.
Why not the others: '24' forgets that the 2 books can swap places (); '36' is an arbitrary product; '120' is total unrestricted arrangements ().
Practise more Algebra and Differential Calculus.
Free questions with an explanation for every one, and full timed Thanawiya Amma (Egypt) mock tests.
More Algebra and Differential Calculus questions
- In the binomial expansion of , what is the term independent of ?
- For , determine the first derivative with respect to for all in…
- If , what is the polar trigonometric form of ?
- What is the limit ?
- If a continuous curve has inflection point at , which statement must be true regarding if it exists?
- Find the slope of the tangent to the curve at the origin .