Question

Four boys picked up 30 mangoes. In how many ways can they divide them, if all mangoes be indentical?

• A. ${}^{33}{C}_3$
• B. ${}^{33}{C}_2$
• C. $5456$
• D. None of these

Answer 1

The correct option is A ${}^{33}{C}_3$

let each boys take $x_1,x_2,x_3,x_4$ numbers of mangoes respectively

So $x_1+x_2+x_3+x_4=30$

if the equation is $x_1,x_2+x_3+...+x_r=n$

Then number of integral solution above is $(\frac{n+r-1}{r-1})$

Here $n=30,r=4$

So number of ways divided is $(\frac{33}{3})$ or ${}^{33}{C}_3$