Number of seven digit positive integers formed using digits 1,2,3 and 4 only and sum of digits equal

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6.Permutation and Combination

hard

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

$414$

(JEE MAIN-2023)

Solution

$x _1+ x _2+ x _3+ x _4+ x _5+ x _6+ x _7=12, x _{ i } \in\{1,2,3,4\}$

No. of solutions $=^{5+7-1} C_{7-1}-\frac{7 !}{6 !}-\frac{7 !}{5 !}=413$

Standard 11

Mathematics

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