Undergrad Combination or Permutation Calculation

[Vector1962]

TL;DR

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.

 

[mjc123]

Choose the number 2. Then the problem reduces to selecting any 3 from 5 numbers.

 

[Vector1962]

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.

 

[FactChecker]

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.