Problem Solving

If i have to chose two specific numbers from a set of 5 numbers:
Eg: 2 and 3 from set {1,2,3,4,5}

I understand the basic counting principle gives 2/5. (2 out of 5)
Using Combinations Will it be 2c2/5c2? or 2c2/5p2?

Hi shashwats,

I hope this is your question - what is the probability of getting a 2 and a 3 when 2 numbers are randomly picked from the set {1,2,3,4,5}. If yes, then here's the solution.

1. The basic counting would give you 20 total possible combinations (remember - (2,3) and (3,2) are different).

Hence you would have 2/20 as your probability.

2. Using formula, it would be 2C2 / 5C2.
You might want to note this.
There might rarely be a situation wherein you would require a combination in the numerator and a permutation in the denominator.

Pls hit 'thank' button if you find my post useful.

I think yiu are confused between two question-
1. How many ways to select two number?
2. what is the probavility that those two selected numbers are 2 and 3?

for 1st question simple answer is 5C2, that is 10. That means if you take two nubers at a time you can mame 10 different selection.

For 2nd question -
you want pair of 2 and 3, so your probability that this one particular pair is chosen out of 10 is 1/10 that is 1/5C2= desired case/total cases.


I think its clear.