JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of seven digit positive integers formed using the digits \(1,2,3\) and \(4\) only and sum of the digits equal to \(12\) is \(...........\).
- A \(412\)
- B \(411\)
- C \(413\)
- D \(414\)
Answer & Solution
Correct Answer
(C) \(413\)
Step-by-step Solution
Detailed explanation
\(x _1+ x _2+ x _3+ x _4+ x _5+ x _6+ x _7=12, x _{ i } \in\{1,2,3,4\}\) No. of solutions \(=^{5+7-1} C_{7-1}-\frac{7 !}{6 !}-\frac{7 !}{5 !}=413\)
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