Question

The number of ways in which $20$ one rupees coins can be distributed among $5$ people such that each person gets at least $3$ rupees, is_____

• A. $26$
• B. $63$
• C. $126$
• D. none of these

Answer 1

The correct option is C $126$

Let $x$ ,$y$,$z$,$v$ and $w$ are $5$ people

$x+y+z+v+w=20$

Such that $x\ge 3,y\ge 3,z\ge 3,v\ge 3,w\ge 3$

Let us give $3$ coins to each

$x+y+z+v+w=20-(3+3+3+3+3)$

$x+y+z+v+w=20-15$

$x+y+z+v+w=5$

Now find no negative interest solution of this equation

Total ways ${=}^{n+r-1}{C}_{r-1}$

${=}^{5+5-1}{C}_{5-1}{=}^g{C}_4=\frac{9\times 8\times 7\times 6}{9\times 3\times 2}=126$