JEE Advanced · Mathematics · 4. P&C
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 55
- B 66
- C 77
- D 88
Answer & Solution
Correct Answer
(C) 77
Step-by-step Solution
Detailed explanation
There are two possible cases arise:
Case I Five 1's, one 2's, one 3's
\(\therefore\) Number of numbers \(=\frac{7 !}{5 !}=42\)
Case II Four 1's, three 2's
\(\therefore\) Number of numbers \(=\frac{7 !}{4 ! 3 !}=35\)
\(\therefore\) Total number of numbers \(=42+35=77\)
Case I Five 1's, one 2's, one 3's
\(\therefore\) Number of numbers \(=\frac{7 !}{5 !}=42\)
Case II Four 1's, three 2's
\(\therefore\) Number of numbers \(=\frac{7 !}{4 ! 3 !}=35\)
\(\therefore\) Total number of numbers \(=42+35=77\)
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