Create nCr.py

Calculate nCr using fermits little theorem

Author: tsaideepak7

math/nCr_computations/python/nCr.py

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+'''
+
+fermits little theorem
+nCr % p = (fac[n]* modinverse(fac[r]) % p *  modinverse(fac[n-r]) % p) % p
+
+modinverse(x) % p = x^p-2
+
+'''
+
+
+def ncr(n, r, p): 
+    numerator = denominator = 1 
+    for i in range(r): 
+        numerator = (numerator * (n - i)) % p 
+        denominator = (denominator * (i + 1)) % p     
+    return (numerator * pow(denominator , p - 2 , p)) % p 
+
+
+n, r, p = 10**5, 20000, 1000000007
+
+print(ncr(n, r, p)) 
+
+
+