Legislative Committee A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic. (a) How many different delegations are possible? (b) How many delegations would have all Democrats? (c) How many delegations would have 2 Democrats and 1 Republican? (d) How many delegations would include at least 1 Republican?

Step-by-step explanation:

GIVEN: Legislative Committee A legislative committee consists of Democrats and Republicans. A delegation of is to be selected to visit a small Pacific island republic.

TO FIND: (a) How many different delegations are possible? (b) How many delegations would have all Democrats? (c) How many delegations would have Democrats and Republican? (d) How many delegations would include at least Republican.

SOLUTION:

(a)

Total members

Total delegation possible

(b)

Total democrats

Total delegation possible with all democrats

(c)

Total democrats

Total republicans

Total delegations with democrats and republican

(d)

Total republicans

Total delegation with at least republican

putting values from part (a)  and (b)

Total delegation with at least republican