Question

I need the right answer!thanks in advance^^ ​

Answer 1

The questions are illustrations of combination and permutation.

The different arrangement of LOVE

From the question, we understand that the letter V must come first.

So, we have:

• First letter = 1; i.e. V
• The second letter can be any of the remaining 3
• The third letter can be any of the remaining 2
• The last letter can be the remaining 1

So, we have:

Arrangement = 1 * 3 * 2 * 1

Arrangement = 6

Hence, there are 6 different arrangement of the letters.

Ways to pick two vegetables

We have:

• Vegetables, n = 5
• To pick, r = 2

The number of different combination is:

Combination = $^5C_2$

Evaluate

Combination = 10

Hence, there are 10 different ways

Number of 4-digit code

The numbers are given as {1,4,5,7,8}

So, we have:

• The first digit can be any of the 5 digits
• The second digit can be any of the remaining 4 digits
• The third digit can be any of the remaining 3 digits
• The fourth digit can be any of the remaining 2 digits

So, we have:

Digits = 5 * 4 * 3 * 2

Digits = 120

Hence, there are 120 different codes of 4-digit

Arrangement of books in a shelf

We have:

• Books, n = 4

The number of arrangement is:

Arrangement = 4!

Evaluate

Arrangement = 24

Hence, there are 24 different arrangements

Outcomes in tossing a coin

A coin has 2 faces

When four coins are tossed, the number of outcomes is:

Outcome = 2 * 2 * 2* 2

Evaluate

Outcome = 16

Hence, there are 16 different outcomes

Ways of sitting in a row

The number of people is given as:

People = 5

So, we have:

• The first person can sit on any of the 5 seats
• The second person can sit on any of the 4 seats
• The third person can sit on any of the 3 seats
• The fourth person can sit on any of the 2 seats
• The last person would sit on the remaining seat1

So, we have:

Ways = 5 * 4 * 3 * 2 * 1

Ways = 120

Hence, there are 120 different ways

Read more about combination and permutation at:

brainly.com/question/11732255

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