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?

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 Link

pinquancaro pinquancaro · Answer 2 · 2019-07-17T08:57:00+02:00

Answer:

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

Step-by-step 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 [tex]^6C_2[/tex]

Solving,

[tex]^6C_2=\frac{6!}{2!(6-2)!}[/tex]

[tex]^6C_2=\frac{6\times 5\times 4!}{2\times 1\times 4!}[/tex]

[tex]^6C_2=3\times 5[/tex]

[tex]^6C_2=15[/tex]

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