In how many ways the 18 English and 12 Hindi books can be kept on the shelf so…
2025
In how many ways the 18 English and 12 Hindi books can be kept on the shelf so that two books on Hindi may not be together.
- A.
15400
- B.
50388
- C.
93564
- D.
None of these
Attempted by 18 students.
Show answer & explanation
Correct answer: B
Interpretation: treat the 18 English books as identical (E) and the 12 Hindi books as identical (H). We count distinct sequences of E and H with no two H adjacent.
Place the 18 English books first. They create 19 gaps (one before the first, one between each pair, and one after the last).
To ensure no two Hindi books are adjacent, place each Hindi book in a different gap. The number of ways to choose 12 gaps from the 19 available is C(19,12).
Compute the binomial coefficient: C(19,12)=C(19,7)=50388.
Answer: 50388