Combinatorics arranging repeated numbers

Question

In the multiset $B=${$5,5,5,7,9,11$}, ¿How many samples of size $3$, without order and without replacement can be extracted of the population?

I think the answer is $8$, but i don't know how to use the formula of combination, because the $5$ is in the set three times. Any hints?

Answer 1

Your answer is correct.

Strategy: Consider cases, depending on the number of fives used.

1. No fives are used: Choose three of the other three numbers in $B$.
2. One five is used: Choose two of the other three numbers in $B$.
3. Two fives are used: Choose one of the other three numbers in $B$.
4. Three fives are used: Choose none of the other three numbers in $B$.

Since the cases are mutually exclusive and exhaustive, add the results to get the total.