Question

The number of ways of selecting $10$ balls out of an unlimited number of white, red, blue and green balls is

• A. $286$
• B. $280$
• C. $120$
• D. $720$

Answer 1

The correct option is A $286$

Formula ${}^{(n+r-1)}{C}_{r-1}$; This means you have to distribute n things among r people where anyone can get any number of things.

This formula is also used to solve algebraic permutation

$X+Y+Z=n$ ; $n\ge 0$

Then number of solution of this equation is also given by the same formula.

So here we have $4$ types of ball Red(R) White(W), Blue(B) and Green(G).

From this we have to select $10$ balls. i.e total which we are going to pick should be equal to $10$.

$R+W+B+G=10$

Number of ways of doing this is ${}^{(10+4-1)}{C}_{4-1}{=}^{13}{C}_3=286$