Combinations possible when choosing 4 or 5 team members from

[zimbabwe]

Homework Statement

How many combinations of people are there if you choose 4 or 5 from a group of 10?

Homework Equations

Relies on binomials

The Attempt at a Solution

binomial (10,4) = binomial (10,6) = 210
But when choosing 5 the answer is binomial (10,5) / 2 = 126
Why do I need to divide by 2?

 

[scottdave]

I am not sure. Is the question to have 10 people, and sometimes you might choose 4 or maybe you choose 5? Then find the total number of combinations.
Could you just have an 11th "person" (person0) which means nobody, then choose 5 from 11? Sometimes one of the five "people" would be nobody, so you would just have 4 people.

 

[Orodruin]

This depends on what divisions of "groups of 5" you consider equivalent. If it does not matter which group of 5 you end up in abcde|fghij is the same division as fghij|abcde. You do not have this issue in the case of splitting into one group of 4 and one of 6. However, if it does matter which group is which (e.g., all people in the first group gets a lollipop and the others do not) then those two divisions would be different and you would not divide by two.