Permutation and combinatorics

[orange.322]

DIRECTION. Solve the following using combination. Show the solution.

Suppose that S = {B, S, C, S, P}, compute for the following and show the resulting combinations of letters.

• The number of subsets of four letters taken all at a time.
• The number of subsets of four letters taken three at a time.
• The number of subsets of four letters taken two at a time.
• The number of subsets of four letters taken one at a time.

 

[Deleted member 4993]

DIRECTION. Solve the following using combination. Show the solution.
Suppose that S = {B, S, C, S, P}, compute for the following and show the resulting combinations of letters.

• The number of subsets of four letters taken all at a time.
• The number of subsets of four letters taken three at a time.
• The number of subsets of four letters taken two at a time.
• The number of subsets of four letters taken one at a time.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Dr.Peterson]

DIRECTION. Solve the following using combination. Show the solution.

Suppose that S = {B, S, C, S, P}, compute for the following and show the resulting combinations of letters.

• The number of subsets of four letters taken all at a time.
• The number of subsets of four letters taken three at a time.
• The number of subsets of four letters taken two at a time.
• The number of subsets of four letters taken one at a time.

The wording almost makes me think this is a joke. First, since the letter S is repeated, the set S is really {B, S, C, P}, consisting of four letters. Then, a "subset of four letters taken k at a time" is not a subset of 4 letters, but presumably a subset of k of the 4 letters in S. If there had actually been 5 letters in the set, "subsets of four letters taken all at a time" would be utter nonsense. It's either intentionally misleading, or just poorly written.

So, how many subsets are there consisting of 4 (all!) of these 4 letters? That's easy to calculate, and even easier to list.

Then do the rest.

 

[pka]

DIRECTION. Solve the following using combination. Show the solution.

Suppose that S = {B, S, C, S, P}, compute for the following and show the resulting combinations of letters.

• The number of subsets of four letters taken all at a time.
• The number of subsets of four letters taken three at a time.
• The number of subsets of four letters taken two at a time.
• The number of subsets of four letters taken one at a time.

@orange.322. Either you have copied this exercise incorrectly or it is a nonsense question,
LOOK at what you wrote: [imath]\bf{{\color{red}S} = \{B, {\color{blue}S}, C, {\color{orange}S}, P \}}[/imath]
That is incorrect notation in any discussion. Please repair it.

 

[Steven G]

S={ B, C, {B,C, {B,C, { ...}}}}

 

[Harry_the_cat]

DIRECTION. Solve the following using combination. Show the solution.

Suppose that S = {B, S, C, S, P}, compute for the following and show the resulting combinations of letters.

• The number of subsets of four letters taken all at a time.
• The number of subsets of four letters taken three at a time.
• The number of subsets of four letters taken two at a time.
• The number of subsets of four letters taken one at a time.

My brain hurts just trying to understand this question!!

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