joint and marginal p.m.f.s

In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date

nonsmokers. 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are

selected randomly and X equals the number who prefer to date nonsmokers and Y equals the

number who prefer to date smokers.

(a) Determine the joint p.m.f. of X and Y. Be sure to include the support of the p.m.f.

$\displaystyle (\frac{7!}{x!7-x!})*(\frac{7-x!}{y!7-x-y!})*(0.78^{x})*(0.01^{y})*(0.21)^{7-x-y}$?

(b) Find the marginal p.m.f. of X. Again, include the support.

$\displaystyle (\frac{7!}{x!7-x!})*(0.78^{x})*(0.21)^{7-x-y}$?

Thank you!