Questions: Counting and Probability Introduction to permutations and combinations Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair (a) How many ways can this be done, if the order of the choices is relevant? (b) How many ways can this be done, if the order of the choices is not relevant?

Counting and Probability Introduction to permutations and combinations Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair (a) How many ways can this be done, if the order of the choices is relevant? (b) How many ways can this be done, if the order of the choices is not relevant?
Transcript text: Counting and Probability Introduction to permutations and combinations Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair (a) How many ways can this be done, if the order of the choices is relevant? (b) How many ways can this be done, if the order of the choices is not relevant?
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Problem Type

Given the order of selection is relevant, we are dealing with a permutations problem.

Step 2: Apply the Permutations Formula

The formula for permutations is given by \(P(n, k) = \frac{n!}{(n-k)!}\).

Step 3: Substitute the Values \(n = 4\) and \(k = 2\)
Calculation: \(P(4, 2) = \frac{4!}{(4-2)!} = 12\)

Final Answer: The number of ways to choose 2 objects from 4 distinct objects is 12.

Step 1: Identify the Problem Type

Given the order of selection is not relevant, we are dealing with a combinations problem.

Step 2: Apply the Combinations Formula

The formula for combinations is given by \(C(n, k) = \frac{n!}{k!(n-k)!}\).

Step 3: Substitute the Values \(n = 4\) and \(k = 2\)
Calculation: \(C(4, 2) = \frac{4!}{2!(4-2)!} = 6\)
Final Answer: The number of ways to choose 2 objects from 4 distinct objects is 6.
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A company purchases inventory or supplies and promises to pay within 30 to 45 days. No formal agreement is signed. The company records this transaction as accounts payable. notes receivable. notes payable. accounts receivable.
failedAnswered
Identify the reaction type for the following reaction. 2 H2O(l) → 2 H2(g) + O2(g) single-displacement double-displacement decomposition synthesis
failedAnswered
If ABCD is dilated by a factor of 1/2, the coordinate of C' would be:
failedAnswered
Teens from low-income families who use multiple types of drugs and commit crimes frequently are studied. Which common characteristic among persistent substance abusers and criminals is illustrated? Poor school performance Rational choice Emotional problems Genetic basis
failedAnswered
Evaluate the limit as x approaches 2 of (2x^2 - 6x + 4) / (-2x^2 - x + 10)