Outcomes - how to determine total possible outcomes

[Guest]

I need help with the following problems. I am in a sixth grade advanced math course and I was not there when the teacher went over this...help!

Seven friends show up at a restaurant and there are only five empty seats. How many combinations of five students can be made from the 7 students that arrived?
I listened to a web tutor who went over permutations. I used that method using 5! or 120. Is that right?

At an ice cream shop you can get a sundae with three of six possible toppings. How many different combinations of three toppings can you obtain from the 6 choices? I came up with eighteen (3/6) but my Dad says I am wrong. nks I am wrong.

A farmer has 6 pigs to feed but only two can eat at a time. How many combinations of the 2 pigs can be made from the 6 pigs. I listed all combinations of the six pigs and came up with 15 combinations. Is that right and is there a formula that can be used for this so I don't have to list all the combinations?

Thanks!

Megan

 

[Guest]

draw a picture, that might help

* ='s seats
$=students

*1 *2 *3 *4 *5 *6 *7

:idea: 1*1$ 2*2$ 3*3$ 4*4$ 5*5$ 6*6$ 7*7$ its an example, try using pictures

just trying to help , since you didn't get any replies .

 

[Gene]

Either P(7,5) or
Any one of 7 in seat 1.
Any one of 6 in seat 2.
Any one of 5 in seat 3.
Any one of 4 in seat 4.
Any one of 3 in seat 5.
P(7,5) = 7*6*5*4*3 or
7!/2!

Same idea at shop.

Same idea at slop except you have to divide by 2 cause the order of pigs doesn't matter.

 

[pka]

Seven friends show up at a restaurant and there are only five empty seats. How many combinations of five students can be made from the 7 students that arrived?

Doesn’t the question say combinations? Where in the question is there anything said about the order in which the students are seated? There is nothing in the statement about order it asks about CONTENT.
\(\displaystyle \L
\left( \begin{array}{l}
7 \\
5 \\
\end{array} \right) = \frac{{7!}}{{\left( {5!} \right)\left( {2!} \right)}}\)

At an ice cream shop you can get a sundae with three of six possible toppings. How many different combinations of three toppings can you obtain from the 6 choices?

A farmer has 6 pigs to feed but only two can eat at a time. How many combinations of the 2 pigs can be made from the 6 pigs. I listed all combinations of the six pigs and came up with 15 combinations. Is that right and is there a formula that can be used for this so I don't have to list all the combinations?

Again it says combinations.