Question

Question 5
5. Write python code for the given for the problem:
Ex: Working group has 8 members. Three will be assigned to lead the group (no difference in leadership
positions). If there are 3 women and 5 men in the group, what is the probability of exactly 1 woman
being assigned to the leadership (if assigned randomly)?

Answer 1

Python code:

import math
def ncr(n,r):
    f=math.factorial
    return f(n)/f(r)/f(n-r)

print("We have to choose 3 leaders out of which exactly one woman")
print("Given 3 women and 5 men in the group")
m=ncr(5,2)*ncr(3,1)
print("Number of ways such that exactly one women and 2 men as Leaders is :",m)
n=ncr(8,3)
print("Total Number of ways such that exactly 3 members as Leaders out of 9 is :",n)
print("Probability is ",m/n)

Execution screenshot:

main.py 1 import nath 2- def ncr(n,r) f-nath.factorial return f(n)/f(r)/f(n-r) 4 6 print("We have to choose 3 leaders out of which exactly one woman") 7 print("Given 3 wonen and 5 men in the group") 8 -ncr (5,2) ncr(3,1) 9 print(" Number of ways such that exactly one women and 2 men as Leaders is:",m) 10 n-ncr(8,3) 11 print("Total Number of ways such that exactly 3 members as Leaders out of 9 is",n) 12 print("Probability is ",n/n) 13 poui: we have to choose 3 leaders out of which exactly one woman Given 3 women and 5 men in the group Number of ways such that exactly one women and 2 men as Leaders is: 30.0 Total Number of ways such that exactly 3 members as Leaders out of 9 is : 56.0 Probability is 0.5357142857142857 . Program finished with exit code θ Press ENTER to exit console.