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.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: