Write each die's value as 6−rᵢ, where rᵢ∈[0,5]. Sum=22 means Σ(6−rᵢ)=22, i.e. Σrᵢ=24−22=2, with each rᵢ≥0 (the upper bound rᵢ≤5 is automatically satisfied since the total is only 2). Number of non-negative integer solutions to r1+r2+r3+r4=2 is C(2+4−1, 4−1) = C(5,3) = 10.