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?

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:

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

There are 35 combinations.

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation: