The number of fish is limited, so every attempt will decrease. That mean the chance will be dependent, but the order is not important.
The number of ways to take 4 fish out of 8 fish would be:
8!/4!(8-4)!= 70 ways
If there is 4 different container and you have 4 fish, then the order is important. The number of ways to do it would be: 4!/(4-4)!= 24 ways.
The total of possible ways of these two event would be: 70 *24= 1680 ways
This can be done in 1680 ways
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Permutation.
A researcher randomly selects 4 fish from among 8 fish in a tank and puts each of the 4 selected fish into different containers.
It means that we arrange 4 objects out of 8 objects.
[tex]^8 P_4 = \frac{8!}{( 8 - 4 )!}[/tex]
[tex]^8 P_4 = \frac{8!}{ 4 !}[/tex]
[tex]^8 P_4 = 5 \times 6 \times 7 \times 8[/tex]
[tex]^8 P_4 = \boxed{1680}[/tex]
This can be done in 1680 ways
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation , Researcher , Fish , Arrangement
