Question

Number of ways in which 15 indistinguishable oranges can be distributed in 3 different boxes so that every box R have atmost 8 oranges, are

• A. 52
• B. 108
• C. 76
• D. 28

Answer 1

The correct option is A

52

Required ways = (Total possible ways without restriction) - (ways when any box can $\ge 9$ oranges)
Total possible ways are
$x+y+z=15$ ${\Rightarrow }^{15+3-1}{C}_{3-1}{=}^{17}{C}_2$
Ways when any box can have 9 oranges $x+y+z=15$
Either one of x, y, z can have more than 9 oranges
Number of ways are ${}^3{C}_1{\times }^{6+3-1}{C}_{3-1}{=}^3{C}_1{\times }^8{C}_2$
Required ways are = ${}^{17}{C}_2{-}^3{C}_1{\times }^8{C}_2=52$