JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is:
- A 429
- B 384
- C 403
- D 455
Answer & Solution
Correct Answer
(D) 455
Step-by-step Solution
Detailed explanation
Let oranges are identical then \(x_1+x_2+x_3+x_4=16\) and \(x_1, x_2, x_3, x_4 \geq 1\) or \(x_1^{\prime}+x_2^{\prime}+x_3^{\prime}+x_4^{\prime}=12\) so total number of solutions are \(={ }^{12+3} C _3={ }^{15} C _3=455\)
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