2.a) Your sample space, S, is all the ways of choosing three dishes from the take away. There are 27 possible dishes to choose from so
n(S) = 27 · 27 · 27 = 19683.
Consider the event, E, that you all choose chicken dishes, then
n(E) = 6 · 6 · 6 = 216.
The probablility that all three of you choose chicken dishes is n(E) / n(S) = 216 / 19683 = 8 / 729. Hence the probablility that the three of you end up with a meal that does not consist only of chicken dishes is
1 - 8 / 729 = 721 / 729.
b) Your sample space is the same as in part a). Here let E be the event that none of you
choose vegetarian dishes. Ignoring the vegetarian dishes, you each have 22 dishes to
choose from, so
n(E) = 22 · 22 · 22 = 10648.
The probability that the three of you end up with a meal that has no vegetarian dishes in it is
P(E) = n(E) / n(S) = 10648 / 19683.