Question

The number of ways of selecting $10$ balls from the unlimited number of red, green, white and yellow balls, if selection must include $2$ red and $3$ yellow balls is

• A. $36$
• B. $56$
• C. $112$
• D. None of these

Answer 1

Answer: (B)

$56$

Number of $10$ balls selections

$=$ coefficients of $x^{10}$ in $(x^2+x^2+...)(1+x+x^2+...)(1+x+x^2+...)(x^3+x^4+...)$

$=$ coefficients of $x^5$ in ${(1+x+x^2+...)}^4$

$=$ coefficients of $x^5$ in ${(1-x)}^{-4}$

${=}^{(4+5-1)}{C}_5{=}^8{C}_5=56$ ways.