Question

A researcher randomly selects 4 fish from among 8 fish in a tank and puts each of the 4 selected fish into different containers. How many ways can this be done?

Answer 1

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

Answer 2

This can be done in 1680 ways

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

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.

$^8 P_4 = \frac{8!}{( 8 - 4 )!}$

$^8 P_4 = \frac{8!}{ 4 !}$

$^8 P_4 = 5 \times 6 \times 7 \times 8$

$^8 P_4 = \boxed{1680}$

This can be done in 1680 ways

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation , Researcher , Fish , Arrangement