binomials

The expression can be simplified by using the fact that binomial coefficients are symmetric, i.e. binom{n}{k} = binom{n}{n-k}. This means that binom{100}{50}/binom{200}{51}*binom{100}{51}/binom{200}{50} can be simplified to binom{100}{50}/binom{200}{50}. Therefore, the simplified expression is binom{100}{50}/binom{200}{50}.