Question

Assume you are trying to choose 5 letters from your name and surname altogether (you can use your name and surname. or can use someone's name and surname). By using the permutation rule, find how many different selection could be made if replacement is allowed and order is not important. By using the combination rule, find how many different selection could be made if replacement is allowed and order is not important. Repeat the same process once for the case when the order is important. you interpret all factors of the formula and explain everything you do in details.

Answer 1

My 5 words are:

SACHI

Using the permutation rule:

Since replacement is allowed and order is not important, every number can be arranged in 5 ways. Let's explain this for the first word S,

S can be placed in 5 ways:

1. SACHI

2. ASCHI

3. ACSHI

4. ACHSI

5. ACHIS

It means each letter can be selected in 5 ways.

Total number of ways = 5*5*5*5*5 since there are 5 letters = 3125 ways

Using the combination rule:

Since replacement is allowed and order is not important, every number can be arranged in 5 ways. Let's explain this for the first word S,

S can be placed in 5 ways:

1. SACHI

2. ASCHI

3. ACSHI

4. ACHSI

5. ACHIS

It means each letter can be selected in 5 ways.

Total number of ways = 5*5*5*5*5 since there are 5 letters = 3125 ways

Thus, when order is not important, the number of ways are equal for permutation and combination method.

When order is important:

S can be placed in 5 ways like discussed above.

Now, S is used, we can now use only the remaining 4 letters,

thus, the number of ways for the second letter are: 4 ways

Similarly, for all, the total number of ways = 5*4*3*2*1 = 120 ways