Question

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

• A. ${}^{13}{C}_3$
• B. $286$
• C. $270$
• D. $86$

Answer 1

Answer: (A), (B)

The correct options are
A ${}^{13}{C}_3$
B $286$

Formula $^{(n+r-1)}\textrm{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

${}^{(10+4-1)}{\text{C}}_{(4-1)}{=}^{13}{\text{C}}_3=286$

Answer