For n ≥ 2 consider the affine Lie algebra sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1 with simple roots {αi∣0 ≤ i ≤ n − 1}. Let sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1 denote the integrable highest weight sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1-module with highest weight kΛ0. It is known that there are finitely many maximal dominant weights of V (kΛ0). Using the crystal base realization of V (kΛ0) and lattice path combinatorics we examine the multiplicities of a large set of maximal dominant weights of the form sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1 where sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1, and k ≥ a + b, sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1, sℓ̂(n)V(kΛ0),k∈ℤ≥1sℓ̂(n)kΛ0−λa,bℓλa,bℓ=ℓα0+(ℓ−b)α1+(ℓ−(b+1))α2+⋯+αℓ−b+αn−ℓ+a+2αn−ℓ+a+1+…+(ℓ−a)αn−1a,b∈ℤ≥1max{a,b}≤ℓ≤n+a+b2−1. We obtain two formulae to obtain these weight multiplicities - one in terms of certain standard Young tableaux and the other in terms of certain pattern-avoiding permutations.