Respuesta :
Answer:
a) 1365 different ways.
b) 126 different ways.
c) 504 different ways.
d) 1239 different ways.
Step-by-step explanation:
The order in which the delegates are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
(a) How many different delegations are possible?
4 delegates from a set of 15. So
[tex]C_{15,4} = \frac{15!}{4!11!} = 1365[/tex]
1365 different ways.
(b) How many delegations would have all Democrats?
4 delegates from a set of 9. So
[tex]C_{9,4} = \frac{9!}{4!5!} = 126[/tex]
126 different ways.
(c) How many delegations would have 3 Democrats and 1 Republican?
3 from a set of 9 and 1 from a set of 6. So
[tex]C_{9,3}*C_{6,1} = \frac{9!}{3!6!}*\frac{6!}{1!5!} = 84*6 = 504[/tex]
504 different ways.
(d) How many delegations would include at least 1 Republican?
Subtract the number of delegations with only democrats(126) from the total(1365). So
1365 - 126 = 1239
1239 different ways.
