Question

In how many ways can $3$ sovereigns be given away when there are $4$ applicants and any applicant may have either $0,1,2$ or $3$ sovereigns?

• A. $15$
• B. $20$
• C. $24$
• D. $48$

Answer 1

The correct option is B $20$

This problem is equivalent to,
No. of non-negative integral solutions of,
$x+y+z+w=3$

Hence the number of required ways is

$={}^{(3+4-1)}{C}_{(4-1)}$

${=}^{6}C{}_3=\frac{6\times 5\times 4}{3\times 2\times 1}$

$=20$

Hence, this is the answer.