### 2022 Q1(3)   2024.7.27

import itertools

def generate_combinations(n, k):
    base_list = [1] * k + [0] * (n - k)
    all_combinations = set(itertools.permutations(base_list))
    return list(all_combinations)

def calculate_intersection(A, B, C):
    return np.mean(np.array(A) & np.array(B) & np.array(C))

def find_min_max_intersection(n, k):
    all_combinations = generate_combinations(n, k)
    min_intersection = 1.0
    max_intersection = 0.0

    for A in all_combinations:
        for B in all_combinations:
            for C in all_combinations:
                intersection_ratio = calculate_intersection(A, B, C)
                if intersection_ratio < min_intersection:
                    min_intersection = intersection_ratio
                if intersection_ratio > max_intersection:
                    max_intersection = intersection_ratio

    return min_intersection, max_intersection

# パラメータを設定
n = 8
k = 6

# 最小値と最大値を計算
min_intersection, max_intersection = find_min_max_intersection(n, k)

min_intersection, max_intersection

(0.25, 0.75)