Answer:
A. 336
B. Arranging 3 people in 8 chairs.
C. 42
B. Arranging 2 people in 7 chairs.
Step-by-step explanation:
A.
[tex]P(n, r) = P(8, 3)[/tex]
Formula for Permutation is given as:
[tex]P(n, r) = \dfrac{n!}{(n-r)!}[/tex]
Putting the value of [tex]n[/tex] = 8 and [tex]r =3[/tex] , we get:
[tex]P(8, 3) = \dfrac{8!}{(8-3)!} \\\Rightarrow \dfrac{8\times 7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 8\times 7 \times 6 \\\Rightarrow 336[/tex]
B. Real world situation for part A:
Arranging 3 people on 8 chairs.
First person has 8 options.
Second person has 7 options.
Third person has 6 options.
C.
[tex]P(n, r) = P(7, 2)[/tex]
Formula for Permutation is given as:
[tex]P(n, r) = \dfrac{n!}{(n-r)!}[/tex]
Putting the value of [tex]n[/tex] = 7 and [tex]r[/tex] = 2 , we get:
[tex]P(7, 2) = \dfrac{7!}{(7-2)!} \\\Rightarrow \dfrac{7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 7 \times 6 \\\Rightarrow 42[/tex]
D. Real world situation for part AC:
Arranging 2 people on 7 chairs.
First person has 7 options.
Second person has 6 options.
