Hi, I have three binomial coefficient problems that I need to prove.
a.) Is (93 Choose 30) greater than, equal to, or less than (93 Choose 31)
b.) Is (93 Choose 30) greater than, equal to, or less than (93 Choose 63)
c.) let a= (99 Choose 4) and let b = (100 choose 95) in terms of a and b.
I know a.) is less then b.) is equal to, and c.) is a+b simply by plugging them into a calculator but is there away to show these are correct without computations? My professor wasn't concerned with the actual values, more so he was looking for the reasoning behind why these are correct without actually computing them. Thank you