What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
cards are of the same colour?
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
cards are of the same colour?
There will be as many ways of choosing $4$ cards from $52$ cards as there are combinations of $52$ different things, taken $4$ at a time. Therefore
The required number of ways $=\,^{52} C _{4}=\frac{52 !}{4 ! 48 !}=\frac{49 \times 50 \times 51 \times 52}{2 \times 3 \times 4}$
$=270725$
$4$ red cards can be selected out of $26$ red cards in $^{26} C _{4}$ ways.
$4$ black cards can be selected out of $26$ black cards in $^{26} C _{4}$ ways.
Therefore, the required number of ways $=\,^{26} C _{4}+^{26} C _{4}$
$=2 \times \frac{26 !}{4 ! 22 !}=29900$
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