find last 3 digits of C(99,19)

Jan 2011
19
0
is there any better way?
97, 89, 83 are primes in [100, 81]
47, 43, 41 are primes in [50, 41] -> 94, 84, 82 in [100, 81]
31, 29 are primes in [33, 27] -> 93, 87 in [100, 81]
23 is the prime in [25, 20] -> 92 in [100, 81].
now process denominator?
below 23 there are primes 19, 17, 13, 11, 7 matching with 95? 85? 91? 88? 84 ?
at last?
99x98x97x47x31x23x89x29x43x83x41x9
at last calculate (mod 1000), end with 594
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
At a glance your method seems like what I'd do, and your answer is correct.