Question

In an examination, the maximum marks for each of the three papers is $50$ each. Maximum marks for the fourth paper is $100$. Find the number of ways in which the candidate can score $605$ marks in aggregate.

• A. $110551$
• B. $210012$
• C. $25000$
• D. $65100$

Answer 1

The correct option is A $110551$

Let a be marks that he looses in section A

Marks obtained $+$ marks lost $=50$

$a+A=50$

$a=50-A$

Similar , $b=50-B$

$C=50-C$

$d=100-D$

$A+B+C+D=150$

$a+b+c+d=100$

$100$ Identical marks $4$ variables

${}^{100+4-1}{C}_{4-1}=\frac{103!}{100!\times 3!}=\frac{101\times 102\times 103}{3\times 2}=101\times 103\times 17=176851$

substracting case $(a=\mathrm{51.......100})$

$=3\times \frac{52!}{49!\times 3!}=66300$

Final Answer : $110551$