Discussion

Explanation:

We know number of ways of distributing n identical objects among r different groups such that each groups gets at least one object is ^n-1C_r-1.

Now,

Case 1: a + b + c = 21.
∴ We need to distribute 21 among 3 different variables a, b & c.
Number of ways of doing this = ^21-1C_3-1 = ²⁰C₂ = 190

Case 2: a + b + c = 22.
Number of ways of doing this = ^22-1C_3-1 = ²¹C₂ = 210

Case 3: a + b + c = 23.
Number of ways of doing this = ^23-1C_3-1 = ²²C₂ = 231

Case 4: a + b + c = 24.
Number of ways of doing this = ^24-1C_3-1 = ²³C₂ = 253

Case 5: a + b + c = 25.
Number of ways of doing this = ^25-1C_3-1 = ²⁴C₂ = 276

∴ Total number of ways = 190 + 210 + 231 + 253 + 276 = 1160

Hence, 1160.

» Your doubt will be displayed only after approval.