Question

There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number ofblack balls to be selected is twice the number of yellow balls, is

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (B)

Let the number of yellow balls be $x$, that of black be $2 x$ and that of green be $y$. Then
$ x+2 x+y=20 \text { or } 3 x+y=20 $
$\Rightarrow y=20-3 x $
$ \text { As } 0 \leq y \leq 20 \text {, we get } 0 \leq 20-3 x \leq 20$
$\Rightarrow 0 \leq 3 x \leq 20 \text { or } 0 \leq x \leq 6$
$\therefore $ The number of ways of selecting the balls is 7 .