An odd subset with two small elements

How many subsets of $\{1, 2, \dots, 10\}$ contain exactly two elements from $\{1, 2, 3\}$ and consist of only odd numbers?

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"Only odd" means eligible elements are $\{1,3,5,7,9\}$ . The odd members of $\{1,2,3\}$ are just $\{1,3\}$ .
Exactly two from $\{1,2,3\}$ forces $\{1,3\}$ ; the rest is any subset of $\{5,7,9\}$ ( $2^3$ ).

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