JEE MAIN - Mathematics (2004 - No. 38)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
$${}^8{C_3}$$
21
$${3^8}$$
5
Explicació
To distribute n objects among p people where everyone should get atleast one object, then number of ways to distribute those n objects
= $${}^{n - 1}{C_{p - 1}}$$
For this question, n = 8 and p = 3
$$ \therefore $$ Number of ways = $${}^{8 - 1}{C_{3 - 1}}$$ = $${}^7{C_2}$$ = 21
= $${}^{n - 1}{C_{p - 1}}$$
For this question, n = 8 and p = 3
$$ \therefore $$ Number of ways = $${}^{8 - 1}{C_{3 - 1}}$$ = $${}^7{C_2}$$ = 21