NIMCET 2025
Number of three-digit numbers that can be formed using 0, 1, 2, 3 and 5, where these digits are allowed to repeat any number of times, is equal to
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Answer: Option B — 100
Detailed Solution
Hundreds digit: 4 choices (not 0). Tens and units: 5 choices each.
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✓ Check
All strings , minus those starting with 0 ( ), gives 100.⚠ Common trap
(C) 125 counts strings with a leading 0, which are not three-digit numbers.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.