Answer with explanation:
Total number of Cards in a Pack of Card =52
There are 13 different denomination in the pack of 52 cards each being 4 in number.
⇒Number of ways of selecting 3 cards out of 4 cards , Since order of choosing of cards is not Important
[tex]=_{3}^{4}\textrm{C}\\\\=\frac{4!}{(4-3)!\times 3!}\\\\=4[/tex]
⇒Number of ways of selecting 2 cards out of 4 cards , Since order of choosing of cards is not Important
[tex]=_{2}^{4}\textrm{C}\\\\=\frac{4!}{(4-2)!\times 2!}\\\\=6[/tex]
Now we have to find eight card hands which consists of three cards of one denomination, three cards of another denomination, and two cards of a third denomination
=As there are 13 cards of different denomination each being 4 in number,so we will choose one among 13 different denomination, then 12 different denomination of card are left, so then we will chose second denomination out of 12, then out of 11 we will choose third denomination.
[tex]=_{1}^{13}\textrm{C}\times _{3}^{4}\textrm{C} \times_{1}^{12}\textrm{C}\times _{3}^{4}\textrm{C} \times_{1}^{11}\textrm{C}\times _{2}^{4}\textrm{C} \\\\=13 \times 4\times 12 \times 4 \times 11 \times 6\\\\=164736[/tex]
Since order of arrangement is not important, if you will choose 2 cards of any denomination first,then three cards of any denomination at second place....you will get the same result.
