Question

There is a test of Algorithms. Teacher provides a question bank consisting of N questions and guarantees all the questions in the test will be from this question bank. Due to lack of time and his laziness, Codu could only practice M questions. There are T questions in a question paper selected randomly. Passing criteria is solving at least 1 of the T problems. Codu can't solve the question he didn't practice. What is the probability that Codu will pass the test?

Answer 1

Language used: Python 3.0

Program:

import math

n=int(input())

for i in range(n):

  N,T,M = map(int,input().split(' '))

  probability=(1-(math.factorial(N-M))/(math.factorial(T)*math.factorial(N-M)))

  #taking in the values of p,q from probability as of p/q

  p,q=probability.as_integer_ratio()

  #creating the multiple inverse of q

  print(pow(q,1000000007-2,1000000007))

Input:

1

4 2 1

Output:

500000004

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