def mycombinations(S, K):
    arr = [0] * K
    cpt = 0
    for i in range(K):
        arr[i] = i 
 
    idx = K - 1     # index in arr (from 0 to K)
    allSets = []
    while True:
        myset = []
        for i in range(K - 1, -1, -1):
            myset.append(S[arr[idx - i]])
        allSets.append(myset)
        
        
        while True:       
            arr[idx] += 1
            while arr[idx] > len(S) - K + idx:
                idx -= 1
                if (idx < 0):                    
                    return allSets
                    
                arr[idx] += 1
                
            while idx < K - 1:
                arr[idx + 1] = arr[idx] + 1   
                idx += 1
                
            else:
                break       
                
    return allSets

N = input()
S = input().split()
K = int(input())
ALLSETS = list(mycombinations(S, K))
COUNT = 0

for c in ALLSETS:
    if 'a' in c:
        COUNT += 1

print(round(COUNT/len(ALLSETS), 11))

from itertools import combinations

N = input()
S = input().split()
K = int(input())
ALL = list(combinations(S, K))
COUNT = sum(1 for UNITS in ALL if 'a' in UNITS)
print(round(COUNT/len(ALL), 4))

from itertools import combinations
n = int(input())
s = list(input().split(" "))
k = int(input())
count = 0
for tup in combinations(s,k):
    if any(elem == 'a' for elem in tup):
        count += 1
print(count / len(list(combinations(s,k))))

from itertools import combinations

length = int(input())
s = input().split()
k = int(input())
count = 0
for tup in combinations(s,k):
    if any(elem == 'a' for elem in tup):
        count += 1

print(count / len(list(combinations(s,k))))