Answer: [tex]\dfrac{2}{7}[/tex]
Step-by-step explanation:
Given : Number of males = 3
Number of females = 4
The number of ways to select a female is elected president and a male is elected vice president :-
[tex]^3P_1\times ^4C_1=\dfrac{3!}{(3-1)!}\times\dfrac{4!}{(4-1)!}=3\times4=12[/tex]
The total number of ways to select 2 people from 7 :_
[tex]^7P_2=\dfrac{7!}{(7-2)!}=42[/tex]
Now, the probability that a female is elected president and a male is elected vice president will be :-
[tex]\dfrac{12}{42}=\dfrac{2}{7}[/tex]
