JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of seven digit integers with sum of the digits equal to \(10\) and formed by using the digits \(1,2\) and \(3\) only is
- A \(42\)
- B \(82\)
- C \(77\)
- D \(35\)
Answer & Solution
Correct Answer
(C) \(77\)
Step-by-step Solution
Detailed explanation
\((I)\) First possiblity is \(1,1,1,1,1,2,3\) required number \(=\frac{7 !}{5 !}=7 \times 6=42\) \((II)\) Second possiblity is \(1,1,1,1,2,2,2\) required number \(=\frac{7 !}{4 ! 3 !}=\frac{7 \times 6 \times 5}{6}=35\) Total \(=42+35=77\)
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