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CAT 2022 Slot 3 · Quant · Permutations, Combinations and Sets · hard

In how many ways can 5 distinct books be distributed among 3 students so that each student gets at least one book?

Single correct option

In how many ways can 5 distinct books be distributed among 3 students so that each student gets at least one book?
  1. A. 125
  2. B. 150
  3. C. 180
  4. D. 243
Show answer and solution

Answer: (B) 150

Total ways without restriction = 3⁵ = 243. Using inclusion-exclusion to remove cases where at least one student gets nothing: 243 − C(3,1)2⁵ + C(3,2)1⁵ = 243 − 96 + 3 = 150. (This counts onto functions/surjections from 5 books to 3 students.)
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Original question written in the CAT 2022 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake