In how many different ways can three persons A, B, C having 6,7 and 8 one rupee coins respectively, donate ₹ 10 collectively?

Step-by-step solution

Total number of ways =[ Number of ways in which ₹ 10 can be distributed among three people] -[Number of ways A can have more than ₹ 6] - [Number of ways B can have more than ₹ 7 ] - [Number of ways C can have more than ₹ 8] Total possibilities = ^ (n+r-1) C_n= (10+3-1) 10 = 12 10 = 12 ! 10 ! 2 ! =66A can have more than 6 in ^5 C₃=10 ways B can have more than 7 in ^4 C₂=6 ways C can have more than 8 in ^3 C₁=3 ways Total number of ways =66-10-6-3=47