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?

Constraints
0 < T <= 10000

0 < N, T <= 1000

0 <= M <= 1000

M,T <= N

Input Format
First line contains single integer T denoting the number of test cases.

First line of each test case contains 3 integers separated by space denoting N, T, and M.

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Answer 1

Lazy student problem

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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