Multiple choice

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a she. If so that the dictionary is always in the middle. Then the number of such arrangements is

  1. at least $500$ but less than $750$
  2. at least $750$ but less than $1000$
  3. at least $1000$
  4. less than $500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Select 4 novels from 6: 6C4 = 15. Select 1 dictionary from 3: 3C1 = 3. Arrange 4 novels and 1 dictionary with dictionary in middle: 4! * 1! = 24. Total = 15 * 3 * 24 = 1080.

AI explanation

Using the method of selection and linear arrangement, we first choose the books to place on the shelf. We select 4 novels out of 6 in 6C4 = 15 ways, and we select 1 dictionary out of 3 in 3C1 = 3 ways, giving 15 * 3 = 45 possible selections of 5 books. Since the dictionary must be in the middle, the 4 novels can be arranged in the remaining 4 positions in 4! = 24 ways. The total number of such arrangements is 45 * 24 = 1080, which is at least 1000.

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