Question
The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 455
- B. 429
- C. 403
- D. 384
Answer
A. 455
Step-by-step solution
Distributing 16 identical oranges to 4 children with each getting at least 1. Let x_i 1 for i = 1,2,3,4 and x_1+x_2+x_3+x_4 = 16. Substituting y_i = x_i - 1 0: y_1+y_2+y_3+y_4 = 12. By stars and bars, number of ways = 12+3 3 = 15 3 = 15 14 13 6 = 455.
Related: Mathematics — Permutation Combination · All PYQ Banks