Answer: a) 124,596, b) 2142691552.
Step-by-step explanation:
Since we have given that
Number of distinguishable balls = 24
Number of boxes = 6
(a) In how many different ways can this be done?
![^{24}C_6\\\\=134,596](https://tex.z-dn.net/?f=%5E%7B24%7DC_6%5C%5C%5C%5C%3D134%2C596)
(b) In how many different ways can this be done if box 1 must get 12 balls, box 2 must get 7 balls, box 3 must get 5 balls, and boxes 4, 5, and 6 must be empty?
Number of ways would be
![\dfrac{24!}{12!7!5!}=2142691552](https://tex.z-dn.net/?f=%5Cdfrac%7B24%21%7D%7B12%217%215%21%7D%3D2142691552)
Hence, a) 124,596, b) 2142691552.