How do you calculate binomial distribution Im confused as to

How do you calculate binomial distribution?

I\'m confused as to when to use a calculator or the binomial table or the formula

Sample question: . Is it more likely to observe eight or more heads in ten flips of a fair coin or to observe
16 heads or more in twenty flips?

Solution

nC_kp^k(1?p)^n?k=

observe eight or more heads in ten flips:(10C₂)?(1/2)⁸?(1/2)²⁺10C₁?(1/2)⁹?(1/2)¹+10C₀?(1/2)¹⁰?(1/2)⁰

16 heads or more in twenty flips^:nC_kp^k(1?p)^n?k

k from 16 to 20