Answer with explanation:
Total number of cards in the deck =50
There are card numbered from 1 to 10 in 5 suits.
We have to calculate 5 card hands in the deck that include exactly one pair of two cards that have the same numeric value
[tex]\rightarrow_{2}^{5}\textrm{C}=\frac{5!}{(5-2)!2!}\\\\=\frac{5!}{(3!)2!}\\\\=\frac{3! \times 4 \times 5}{3! \times 2!}\\\\=\frac{20}{2}\\\\=10[/tex]
So, if you will find pairs in each card numbered from 1 to 10, there will be 10 distnct pairs if there are 5 suits of each card.
