In [10]:

    

def countWays(n):
    if n<0:
        return 0
    elif n==0:
        return 1
    else: 
        return countWays(n - 1) + countWays(n - 2) + countWays(n - 3)


    

In [12]:

    

countWays(3)


    

    
Out[12]:





4

In [13]:

    

def pascal(n):
    if n < 1:
        return []
    if n == 1:
        return [1]
    else:
        p_line = pascal(n-1)
        line = [ p_line[i]+p_line[i+1] for i in range(len(p_line)-1)]
        line.insert(0,1)
        line.append(1)
    return line

for i in range(1,6):
    print(pascal(i))


    

    




[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]

In [17]:

    

def birthday(n):
    prob = 1
    for i in range(1, n):
        prob = prob * (float(365 - i) / 365)
    return (1 - prob)*100


    

In [19]:

    

birthday(365)


    

    
Out[19]:





100.0

In [ ]: