[JEE Advanced 2009] the number of seven digit integers with digit sum 10 using only 1 2
The number of seven-digit integers with digit sum $10$, using only $1,2,3$, is
(a) $55$
(b) $66$
(c) $77$
(d) $88$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (c) $77$
Counts $(a,b,c)$ of $1,2,3$ with $a+b+c=7,a+2b+3c=10\Rightarrow b+2c=3$: $(4,3,0)\to\frac{7!}{4!3!}=35$, $(5,1,1)\to\frac{7!}{5!}=42$. Total $77$.
JEE Advanced 2009 · Permutations and Combinations — verified solution by the Vidaara Team.
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