Question

$12$ identical things can go into $5$ purses. No purse remains empty. The number of ways are

• A. ${}^{11}{C}_5$
• B. ${}^{12}{C}_5$
• C. ${}^{11}{C}_4$
• D. ${}^{12}{C}_4$

Answer 1

Answer: (C)

${}^{11}{C}_4$

$\therefore$ No. of ways of $12$ identical things go in $5$ purse so that no purse is empty is same as number of nonzero positive integral solution of
$x_1+x_2+x_3+x_4+x_5=12-5$
$x_1+x_2+x_3+x_4+x_5=7$
$n=7;r=5$
No. of ways $={}^{n+r-1}{C}_{r-1}={}^{11}{C}_4$