A certain legislative committee consists of 10 senators. A subcommittee of 3 senators is to be randomly selected.
a. How many different such subcommittees are there?
b. If the senators are ranked 1, 2, . . . , 10 in order of seniority, how many different subcommittees would include the most senior senator?
c. What is the probability that the selected subcommittee has at least 1 of the 5 most senior senators?
d. What is the probability that the subcommittee includes neither of the two most senior senators?