There are 9*8*7 = 504 ways.
30 = 6 * 5 if we assume the president and the vice-president must be different people.
120
Assuming the order matters, you have 22 options for the president; after that position is assigned you still have 21 options for the vice-president, and then 20 options for the secretary; so the total is 22 x 21 x 20.
40 x 39 x 38 x 37 = 2193360
There are 9*8*7 = 504 ways.
No ex-president has later become a Secretary of State- six have moved up from Secretary of State to president, however.
15
125
The answer is 15 * 14 * 13 = 15 P 3 = 780 IF you assume that no one person can hold two offices at once and that all in the group are qualified for any office.
6,375,600
309*308/2 = 47586
The position of secretary of state is a cabinet position and is appointed by the President of the United States. Each term is four years and the President could appoint the secretary of State for two terms.
At the beginning of each new session of Congress, members of both parties decide how many members of each will be assigned to the committee. Members of Congress express their preferences for committee assignments and the whole body votes on the final committee makeup.
30 = 6 * 5 if we assume the president and the vice-president must be different people.
There are many different government agencies, and each of them is headed by a secretary. That secretary typically is a part of the president's cabinet and acts as a presidential advisor.
No times. The senate has never chosen the vice-president. In 1824 when no candidate for president got a majority, John C. Calhoun still won a majority of the electoral vote for vice-president.