Find the number of ways of distributing 12 chocolates among 3 students such that no student can get more than 7 chocolates.

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Solution

The correct option is B 46
Total no. of ways when restriction is not there = $^{14} C_{2}$ .
when a > 7, it is an invalid case
put a = x + 8
x + 8 + b + c = 12
x + b + c = 4
This can be done in $^{6} C_{2}$ ways
Similarly, for cases where b, c >7, there are $^{6} C_{2}$ ways
Therefore, total count is: $^{14} C_{2}$ - 3* $^{6} C_{2}$ = 91 - (3*15) = 46

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