Respuesta :
Each of these is a combination probability. First, we need to find the total number of ways the people can be selected. Then, divide it by the number of ways they can be rearranged within the group.
Here are the answers:
2 people = 120 groups
4 people = 1820 groups
6 people = 8008 groups
3 people = 560 groups
1 person = 16 groups
Here are the answers:
2 people = 120 groups
4 people = 1820 groups
6 people = 8008 groups
3 people = 560 groups
1 person = 16 groups
The number of ways 16 people can be divided into five groups containing 2,4,6,3 and one people respectively is 120, 1820, 8008, 560, and 16 respectively.
It is given that the 16 people be divided into five groups containing respectively 2,4,6,3 and one person.
It is required to find the In how many ways can 16 people be divided into five groups.
What are permutation and combination?
A permutation can be defined as the number of ways a set can be arranged, order matters but in combination, the order does not matter.
The formula for calculating the number of combinations:
[tex]\rm _{n}^{}\textrm{C}_r =\frac{n!}{r!(n-r)!}[/tex]
Where n = Number of elements in the set
r = Number of selected elements from the set
C = number of combination.
We have a number of people n = 16
If the number of persons r = 2, then
[tex]\rm _{16}^{}\textrm{C}_2 =\frac{16!}{2!(16-2)!}[/tex] ⇒120
If the number of people r = 4, then the number of combinations:
[tex]\rm _{16}^{}\textrm{C}_4 =\frac{16!}{4!(16-4)!}[/tex] ⇒ 1820
If the number of people r = 6, then the number of combinations:
[tex]\rm _{16}^{}\textrm{C}_6 =\frac{16!}{6!(16-6)!}[/tex] ⇒ 8008
If the number of people r = 3, then the number of combinations:
[tex]\rm _{16}^{}\textrm{C}_3 =\frac{16!}{3!(16-3)!}[/tex] ⇒ 560
If the number of people r = 1, then the number of combinations:
[tex]\rm _{16}^{}\textrm{C}_1 =\frac{16!}{1!(16-1)!}[/tex] ⇒ 16
Thus, the number of ways 16 people can be divided into five groups containing 2,4,6,3 and one people respectively are 120, 1820, 8008, 560, and 16 respectively.
Learn more about combination here:
https://brainly.com/question/4546043
