You have a box of tacks for which it has been determined that if you toss them on the floor precisely 36% will land point up.
How many of these tacks could you toss to make the most likely result be that 10 of them will land point up.
.36n between 9.5 and 10.5
n between 26.4 and 29.2
n = 27, 28, 29 all lead to 10 being the most likely result
This is only an approximation, but it happens to match Charlie's true results.
On the other hand, the approximation method does not (this time) correctly find the n which maximizes the probability.
10/.36 = 27.77, which rounds to 28. As Charlie has demonstrated, however, we are more likely to have 10 up tacks with 27 thrown than with 28.