NIMCET 2018
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into the 3 small boxes. The number of ways of arranging one ball in each of the boxes is
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — 17280
Detailed Solution
The 5 large balls must go into the 6 big boxes: ways.
The other 4 balls fill the remaining 4 boxes (3 small and 1 big) in ways.
Total .
✓ Check
Fill the 3 small boxes first from the 4 small balls ( ), then the 6 remaining balls in the 6 big boxes ( ): .⚠ Common trap
(A) 18720 uses the same digits as 17280 in a different order; multiply carefully.Quick tip
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Permutations & Combinations — Preparation
This question tests your understanding of Permutations & Combinations, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Permutations count arrangements where order matters, while combinations count selections where order does not matter. This topic covers the fundamental principle of counting, factorials, nPr and nCr, arrangements of letters in a word (including repeated letters), circular arrangements, and selecting committees or teams with conditions. The hardest part is deciding whether a question needs a permutation or a combination. Ask yourself whether swapping two chosen items gives a new outcome. If it does, order matters. Conditions such as "two people must sit together" are handled by treating them as a single unit, and "at least one" questions are usually easiest to solve as total minus none. Practise the permutation and combination questions below, each with a step-by-step solution showing how to set up the count.