Question

Statement 1: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is ${{}^{9}C}_3$.
Statement 2: The number of ways of choosing any $3$ places from $9$ different places is ${{}^{9}C}_3$

• A. Statement 1 is true and Statement 2 is false
• B. Statement 1 is false and Statement 2 is true
• C. Statement 1 is true and Statement 2 is true; statement 2 is a correct explanation for statement 1
• D. Statement 1 is true and Statement 2 is truestatement 2 is a not correct explanation for statement 1

Answer 1

The correct option is B Statement 1 is false and Statement 2 is true

$1)$Let no .of balls in first box is $x$,second is $y$,third is $z$,fourth is $p$

$x+y+z+p=10,x\ge 1,y\ge 1,z\ge 1,p\ge 1$

$(x-1)+(y-1)+(z-1)+(p-1)=6$

no of ways of arranging is ${}^{6+4-1}{C}_6{=}^9{C}_6{=}^9{C}_3$

$2)$ number of ways of choosing any $3$ places from $9$ different places is ${}^9{C}_3$