President Barack H. Obama\'s cabinet consisted of the Secretaries of Agriculture

Question

President Barack H. Obama's cabinet consisted of the Secretaries of Agriculture, Commerce, Defense, Education, Energy, Health and Human Services, Homeland Security, Housing and Urban Development, Interior, Labor, State, Transportation, Treasury, Veterans Affairs, and the Attorney General. Assuming that President Obama had 26 candidates, including Hillary Clinton, to fill these posts (and wished to assign no one to more than one post), complete the following sentences. (a) The sample space is the set of all lists of people chosen from (b) The event that Hillary Clinton is the Secretary of State is the set of all lists of 15 people chosen from in which Hillary Clinton occupies (Secretary of State) position.

Explanation / Answer

(a) The sample space is the set of all lists of 15 people chosen from 26 people.

(b) Since, the state is at the eleventh position, therefore who-so-ever will be chosen (selected) for state secretary will be at eleventh position. If the Hillary Clinton is chosen or the secretary position, then the list of 15 people will be formed from Hillary and other 14 peopele from the remaining 25 people.

[Note that if any other person for the post of state secretary may be chosen then 15 people will be chosen from the available 26 people.]

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