Question

Given a 50 card deck with cards numbered from 1 through 10 in each of 5 suits, how many 5 card hands are there that include exactly one pair of two cards that have the same numeric value?

Answer 1

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

`\rightarrow_(2)^(5)\textrm{C}=(5!)/((5-2)!2!)\\\\=(5!)/((3!)2!)\\\\=(3! * 4 * 5)/(3! * 2!)\\\\=(20)/(2)\\\\=10`

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.