Combination or Permutation Calculation

In summary, the conversation discusses selecting 4 items from a set of numbers 1 through 6, with the requirement that the subset must include the number 2. The speaker shares their quick calculation of 15 distinct subsets but mentions the need to exclude those without the number 2. They ask if there is a formula or if they have to create a tree diagram to list the subsets. Another speaker suggests choosing the number 2 first, then selecting 3 from the remaining 5 numbers. The first speaker confirms this method and also shares that they made a tree diagram to arrive at the same solution. The conversation ends with a note on terminology and the difference between combinations and permutations.
  • #1
Vector1962
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TL;DR Summary
How to calculate subsets of 4 items from a set of 6 items and only count the subsets that have a specific item.
Hello Forum:
I have numbers 1 through 6 from which i must select 4 items. The twist is that i need to count only those subsets that include the number 2 all of the subsets are 'distinct' --> 2145 is the same as 2415. My quick calculation yields 15 distinct subsets however some of those do not contain the number 2. is there a formula to use or will i have to make some kind of tree diagram to list them? thanks in advance for the help. also, i picked intermediate but it may be a pretty basic question.
 
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  • #2
Choose the number 2. Then the problem reduces to selecting any 3 from 5 numbers.
 
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Likes Dale
  • #3
Excellent... thank you. for what it's worth and for the number of items involved i made the tree diagram and arrive at exactly what you suggest.
 
  • #4
Just a word about terminology before leaving this. Instead of saying " all of the subsets are 'distinct' --> 2145 is the same as 2415. ", you should say that order doesn't count. Those are the magic words that we look for to determine that it is a problem about the number of combinations. If order counts (2145 not the same as 2415), then it is a problem about the number of permutations.
 

What is the difference between combination and permutation?

Combination and permutation are both mathematical concepts that involve selecting and arranging items from a group. The main difference between the two is that combination is concerned with the selection of items without regard to their order, while permutation involves arranging the selected items in a specific order.

How do you calculate the number of combinations?

The formula for calculating the number of combinations is nCr = n! / (r! * (n-r)!), where n represents the total number of items in the group and r represents the number of items being selected. This formula is also known as the combination formula.

What is the formula for calculating permutations?

The formula for calculating permutations is nPr = n! / (n-r)!, where n represents the total number of items in the group and r represents the number of items being selected. This formula is also known as the permutation formula.

What is the difference between nCr and nPr?

The main difference between nCr and nPr is that nCr calculates the number of combinations, while nPr calculates the number of permutations. In other words, nCr is used when order does not matter, and nPr is used when order does matter.

What are some real-life applications of combination and permutation calculation?

Combination and permutation calculation are used in various fields such as statistics, probability, and computer science. Some real-life applications include calculating the number of possible outcomes in a game of chance, creating secure passwords, and analyzing data in surveys and experiments.

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