in how many ways can 9 identical balls be distributed among four baske

There are 2 important equations for these types of arrangements


If the number of non negative integer solutions for the equation \(x_1 + x_2 \space + \space ..+ \space x_n \space = \space n\), then the number of ways the distribution can be done is:


(i) \(^{n+r−1}C_{r−1}\). In this case, value of any variable can be zero.


(ii) \(^{n−1}C_{r−1}\). In this case, minimum value for any variable is 1.




Given that: n = 9 balls, r = 4 boxes and and each box should have at least one ball.

Therefore the total number of ways = \(^{n-1}C_{r-1} = \space ^{9-1}C_{4-1} = \space ^8C_3 = \frac{8 \space * \space 7 \space * \space 6}{3 \space * \space 2 \space * \space 1} = 56\)


Option B

Arun Kumar