Find the density function for X.?

Question

A bag contains 3 dimes and 2 nickles. Two coins are selected simultaneously and at random. Let X be the random variable whose value is the value in cents of the 2 coins selected.

Answer 1

There's 3 possibilities
1. X = 20, 2 dimes
2. X = 15, 1 dime 1 nickle
3. X = 10, 2 nickles

Number of different combinations: 5C2 = 5 * 4 / 2 * 1 = 10

P(X = 20) :
Number of ways of picking 2 dimes out of the 3: 3C2 = 3*2*1/2*1 = 3
Probability = 3/10

P(X = 15):
Number of ways of picking 1 coin each, 3 * 2 = 6
Probability 6/10

P(X = 10)
Number of ways of picking 2 nickles = 1
Probability 1/10

So, listed in chart form:
X, P(X)
10, 1/10
15, 6/10
20, 3/10