ten students belong to a school club. Five of the members are juniors. If 2 students are chosen at random to serve as club officers, what is the probability that the officers will both be juniors?

Question

ash2326 · Answer

Total 10 students
5 members are juniors
We have to choose 2 students
Do you know combinations @erica123 ?

anonymous · Answer

no i need help on that

anonymous · Answer

no its a multiple choice question 
A. 1/5 
B. 2/9
. 5/18
D. 2/5

anonymous · Answer

b 2/9

anonymous · Answer

i need to know how!

anonymous · Answer

i dont want just the answer

ash2326 · Answer

Good erica, I'll explain you

ash2326 · Answer

First tell me the probability of choosing 1 junior from these 10 ( you know that there are 5 juniors among the 10)@erica123

anonymous · Answer

choose 2 juniors  from 5 = C(5,2) = 10
and n(S) = C(10,2) = 45
so the prob = 10/45 = 2/9

anonymous · Answer

1/2 ? 
isnt it 5/10 are juniors?

anonymous · Answer

ill tell u how , the chance for choosing the 1st student and hes /shes junior is 5/10 
the chance for choosing the 2st student and hes /shes junior is 4/9
5/10 * 4/9 = 2/9 #

ash2326 · Answer

Yeah it's 1/2
Now choose 1 more junior from 9 people ( we have  4 juniors  now)
@erica123

anonymous · Answer

4/9

anonymous · Answer

wait why isnt it from 10 ?

ash2326 · Answer

Because we have already chosen 1 junior
so we have 9 people now

anonymous · Answer

ohh ok so its 4/9 but what do i do now? do i add subtract/ multiply those fractions

ash2326 · Answer

You need to multiply the two probabilities

anonymous · Answer

20/90

ash2326 · Answer

So what's the correct option?

anonymous · Answer

B. 2/9 because you can simplify 20/90 ?

ash2326 · Answer

Yeah:) you're right
Did you understand?

anonymous · Answer

yes :) thanks so much! you're a great help! =)

ash2326 · Answer

You're welcome:D