
    Determine the number of possible ways to group different learning objectives into adaptive difficulty levels for student pathways. Given n distinct skill components, calculate how many different arrangements of these components into any number of difficulty groups are possible, where each component must be assigned to exactly one difficulty group and empty groups are not allowed.
    

    
def bell_number(n):
    """
    Determine the number of possible ways to group different learning objectives into adaptive difficulty levels for student pathways. Given n distinct skill components, calculate how many different arrangements of these components into any number of difficulty groups are possible, where each component must be assigned to exactly one difficulty group and empty groups are not allowed.
    

    """
def bell_number(n):
    """
    Determine the number of possible ways to group different learning objectives into adaptive difficulty levels for student pathways. Given n distinct skill components, calculate how many different arrangements of these components into any number of difficulty groups are possible, where each component must be assigned to exactly one difficulty group and empty groups are not allowed.
    

    """
    bell = [[0 for i in range(n + 1)] for j in range(n + 1)]
    bell[0][0] = 1
    for i in range(1, n + 1):
        bell[i][0] = bell[i - 1][i - 1]
        for j in range(1, i + 1):
            bell[i][j] = bell[i - 1][j - 1] + bell[i][j - 1]
    return bell[n][0]