Question

Algebra Probability PLEASE HELP***

You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win. How many possible pairs of friends could be chosen in this way?

Answer 1

Answer: 2 friends/1 pair

Explanation:

Mainly because if you do the math, a pair of friends is 2. Knowing that there is 2 short straws (Which if those are the ones that are chosen you get to go), and 4 long straws. Only 2 friends are going to draw the short straws.

Hope this helped :)

Answer 2

15 possible pairs of friends could be chosen in this way.

Explanation:

Given : You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win.

To find : How many possible pairs of friends could be chosen in this way?

Solution :

Total number of friends = 6

The space in the car is for 2 person.

Since, the order doesn't matter we have to choose 2 people out of 6 so we apply combination.

As There are 4 long and 2 short straws, and the short straws win.

i.e. that 2 friends were chosen.

So, Possible ways to find the pairs of friends is
`^6C_2`

Solving,

`^6C_2=(6!)/(2!(6-2)!)`

`^6C_2=(6* 5* 4!)/(2* 1* 4!)`

`^6C_2=3* 5`

`^6C_2=15`

Therefore, 15 possible pairs of friends could be chosen in this way.