The questions are illustrations of combination and permutation.
<h3>The different arrangement of LOVE</h3>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.
<h3>Ways to pick two vegetables</h3>We have:
- Vegetables, n = 5
- To pick, r = 2
The number of different combination is:
Combination =
Evaluate
Combination = 10
Hence, there are 10 different ways
<h3>Number of 4-digit code</h3>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
<h3>Arrangement of books in a shelf</h3>We have:
- Books, n = 4
The number of arrangement is:
Arrangement = 4!
Evaluate
Arrangement = 24
Hence, there are 24 different arrangements
<h3>Outcomes in tossing a coin</h3>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
<h3>Ways of sitting in a row</h3>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
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