This is an example of what I call
number of distributions * probability/distribution:
The number of distributions, or ways to organize, three Hs and three Ts (HHHTTT, HHTHTT, etc.) is the factorial of the total number of terms (6) divided by the factorial of each of the sets of repeated terms (3 Hs and 3 Ts, naturally).
6!/(3!3!) = 20
The probability/distribution is a sample-case probability for ONE of these (not that it matters since the coin toss will always produce a probability of 1/2 per toss):
H H H T T T ==> (1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = (1/2)^6 = 1/64
So that means that...
number of distributions * probability/distribution = 20*1/64 = 20/64 = 5/16.
Answer C.If you're interested in more on this technique, I've written an extensive article about it here:
https://privategmattutor.london/gmat-probability-number-of-distributions-x-probability-per-distribution/