Question

There is money to send four of seven city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the seven who want to go to the conference?

Answer 1

Answer:

There are 35 combinations.

Step-by-step explanation:

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

The formula for determining the number of possible arrangements by selecting only a few objects from a set with no repetition is expressed in the following way:

                                             $C(n,r)=\frac{n!}{( r! (n - r)! )}$

Where:

n – the total number of elements in a set.

r – the number of selected objects.

! – factorial.

So, we want to find how many different combinations of four council members (r = 4) can be selected from the seven (n = 7) who want to go to the conference.

Applying the above formula, we get that

$C(n,r) = C(7,4)=\frac{7!}{( 4! (7 - 4)! )}=\frac{210}{6}=35$

There are 35 combinations.