JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of integers, between \(100\) and \(1000\) having the sum of their digits equals to \(14\) , is ............
- A \(60\)
- B \(45\)
- C \(27\)
- D \(70\)
Answer & Solution
Correct Answer
(D) \(70\)
Step-by-step Solution
Detailed explanation
\(\mathrm{N}=\mathrm{abc}\) (\(i\)) All distinct digits \( a+b+c=14 \) \( a \geq 1 \) \( b, c \in\{0 \text { to } 9\}\) by hit and trial : \(8\) cases \((6,5,3)\) \((8,6,0)\) \((9,4,1)\) \((7,6,1)\) \((8,5,1)\) \((9,3,2)\) \((7,5,2)\) \((8,4,2)\) \((7,4,3)\) \((9,5,0)\) (\(ii\))…
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