Respuesta :
Answer:
120 ways
Step-by-step explanation:
We have a total of 6 people, and we want to form groups of 3, so we can do a combination of 6 choose 3.
But inside a group of 3 people, we need to choose the office of each one, and the number of possibilities for this is calculated using factorial.
So, we have the following:
Number of groups of 3 among 6 people:
C(6,3) = 6!/(3!*3!) = 6*5*4/6 = 20
Different offices inside the group of 3:
3! = 3*2 = 6
Then, to find the total number of possibilities that offices can be filled, we multiply these results:
20 * 6 = 120
(This problem can also be solved using permutation, as the order of the elements in the group matters:
P(6,3) = 6!/3! = 6*5*4 = 120)
In 120 ways can those offices be​ filled.
Given that,
A club with six members is to choose three​ officers:
If each office is to be held by one person and no person can hold more than one​ office.
We have to find,
In how many ways can those offices be​ filled.
According to the question,
Total number of members = 6
Total number group want to form = 3
Then, It is a combination of 6 to choose 3.
Inside a group of 3 people, choose the office of each one, and the number of possibilities for this is calculated using factorial.
Therefore,
Number of groups of 3 among 6 people:
[tex]^6C_3 = \frac{6!}{(6-3!)3!} = \frac{720}{36} = 20[/tex]
Different offices inside the group of 3:
[tex]3! = 3\times 2 \times1 = 6[/tex]
The total number of possibilities that offices can be filled, we multiply these results:
[tex]= 20 \times 6 = 120[/tex]
By using permutation, as the order of the elements in the group matters:
[tex]^6P_3 = \dfrac{6!}{3!} = 6\times5\times4 = 120[/tex]
Hence, In 120 ways can those offices be​ filled.
To know more about Combination click given below.
https://brainly.com/question/11234923
