Math / Discrete

Question4. In how many ways can 5 people be arranged in a line?

Studdy Solution

STEP 1

Assumptions
1. We have 5 distinct people to arrange.
2. We are arranging all 5 people in a single line.
3. The order of arrangement matters, meaning different sequences count as different arrangements.

STEP 2

To determine the number of ways to arrange 5 people in a line, we need to calculate the number of permutations of 5 distinct objects.

STEP 3

The formula to calculate permutations of $n$ distinct objects is given by the factorial of $n$ , denoted as $n!$ .

STEP 4

For our problem, $n = 5$ . Therefore, we need to calculate $5!$ .

STEP 5

Calculate $5!$ using the definition of factorial:
$5! = 5 \times 4 \times 3 \times 2 \times 1$

STEP 6

Perform the multiplication step-by-step:
$5 \times 4 = 20$
$20 \times 3 = 60$
$60 \times 2 = 120$
$120 \times 1 = 120$

STEP 7

Thus, the number of ways to arrange 5 people in a line is 120.

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Question4. In how many ways can 5 people be arranged in a line?

Studdy Solution

STEP 1

Assumptions
1. We have 5 distinct people to arrange.
2. We are arranging all 5 people in a single line.
3. The order of arrangement matters, meaning different sequences count as different arrangements.

STEP 2

To determine the number of ways to arrange 5 people in a line, we need to calculate the number of permutations of 5 distinct objects.

STEP 3

The formula to calculate permutations of $n$ distinct objects is given by the factorial of $n$ , denoted as $n!$ .

STEP 4

For our problem, $n = 5$ . Therefore, we need to calculate $5!$ .

STEP 5

Calculate $5!$ using the definition of factorial:
$5! = 5 \times 4 \times 3 \times 2 \times 1$

STEP 6

Perform the multiplication step-by-step:
$5 \times 4 = 20$
$20 \times 3 = 60$
$60 \times 2 = 120$
$120 \times 1 = 120$

STEP 7

Thus, the number of ways to arrange 5 people in a line is 120.

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Question4. In how many ways can 5 people be arranged in a line?

Studdy Solution

STEP 1

Assumptions1. We have 5 distinct people to arrange.2. We are arranging all 5 people in a single line.3. The order of arrangement matters, meaning different sequences count as different arrangements.

STEP 2

To determine the number of ways to arrange 5 people in a line, we need to calculate the number of permutations of 5 distinct objects.

STEP 3

The formula to calculate permutations of n n n distinct objects is given by the factorial of n n n, denoted as n! n! n!.

STEP 4

For our problem, n=5 n = 5 n=5. Therefore, we need to calculate 5! 5! 5!.

STEP 5

Calculate 5! 5! 5! using the definition of factorial:5!=5×4×3×2×1 5! = 5 \times 4 \times 3 \times 2 \times 1 5!=5×4×3×2×1

STEP 6

Perform the multiplication step-by-step:5×4=20 5 \times 4 = 20 5×4=2020×3=60 20 \times 3 = 60 20×3=6060×2=120 60 \times 2 = 120 60×2=120120×1=120 120 \times 1 = 120 120×1=120

STEP 7

Thus, the number of ways to arrange 5 people in a line is 120.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. We have 5 distinct people to arrange.
2. We are arranging all 5 people in a single line.
3. The order of arrangement matters, meaning different sequences count as different arrangements.

The formula to calculate permutations of $n$ distinct objects is given by the factorial of $n$ , denoted as $n!$ .

For our problem, $n = 5$ . Therefore, we need to calculate $5!$ .

Calculate $5!$ using the definition of factorial:
$5! = 5 \times 4 \times 3 \times 2 \times 1$

Perform the multiplication step-by-step:
$5 \times 4 = 20$
$20 \times 3 = 60$
$60 \times 2 = 120$
$120 \times 1 = 120$