Question

The number of ways in which $13$ non-distinguishable books can be distributed among $7$ students so that every student get at least one book and at least one student gets $4$ books but not more, is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

• A. $341$
• B. $351$
• C. $343$
• D. $371$

Answer 1

The correct option is D $371$

$\left(i\right)4411111$
No. of ways $={}^7{C}_2=21$
$\left(ii\right)4321111$
No. of ways $={}^7{C}_3\times 3!=210$
$\left(iii\right)4222111$
No. of ways $={}^7{C}_1\times {}^6{C}_3=140$

Total number of ways $=21+210+140=371$