Anyone Can Help Me Understand This Problem?

[kavehfa]

Hello Everybody,

I am new to this forum and I hope I am posting this problem in the right place. I would really appreciate it if anyone could help me to solve this problem and understand similar questions.

-If a club has 10 member and 3 are to be chosen to be delegates to a conference, what is the probability that Sara, a member of the club be one of the delegates?

[Rahul@gurome]

Solution:
Required probability is (total number of favorable outcomes)/(total number of all possible outcomes).
Total number of all possible outcomes is 10C3 = 120.
For calculating the total number of favorable outcomes, we need to note that Sara will always be one of the delegates. So we need to select the other 2. This can be done in 9C2 = 36 ways.
So required probability is 36/120 = 3/10

[kavehfa]

Thanks a lot for the answer. Is there any way we can differentiate between permutation and combination when we see a question?

[Rahul@gurome]

Thanks a lot for the answer. Is there any way we can differentiate between permutation and combination when we see a question?

If the question is asking about arrangement, go for permutation and if the question is asking about selection where order does not matter, go for combination.
This particular problem is talking about selection of delegates.
Hence we use the combination concept.

[kavehfa]

Thanks again!