Respuesta :
Answer:
The number of ways Tony and Maria can both be selected for the committee is 8 ways.
Step-by-step explanation:
i) Tony and Maria have to be on the committee together or not at all.
ii) Let us consider Tony and Maria as combined as one person.
Therefore now we can say that the number of eligible people for the committee = 9 - 1 = 8.
iii) therefore the number of ways that both Tony and Maria can be selected for the committee are
= 8C1 = [tex]\hspace{0.2cm}\binom{8}{1} = \frac{8!}{1! (8-1)!} = \frac{8!}{1!\times 7!} = \frac{8}{1} = \hspace{0.1cm}8 \hspace{0.1cm}ways[/tex]
The number of ways to select exactly one of Tony and Maria is 70.
It is given that,
- The number of eligible people is 9.
- The number of members required for the committee is 4.
- Exactly one of Tony and Maria be selected for the committee.
Explanation:
Excluding Tony and Maria from the 9 people. The number of remaining people is 7.
Exactly one of Tony and Maria be selected for the committee. So, one person is selected from 2 and 3 people are selected from the remaining 7 people.
[tex]\text{Number of ways}=^2C_1\times ^7C_3[/tex]
[tex]\text{Number of ways}=\dfrac{2!}{1!(2-1)!}\times \dfrac{7!}{3!(7-3)!}[/tex]
[tex]\text{Number of ways}=2\times 35[/tex]
[tex]\text{Number of ways}=70[/tex]
Thus, the number of ways to select exactly one of Tony and Maria is 70.
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