The unique four card combinations in a deck of cards when all queens are removed is 4,669,920.
What is permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
For the given situation,
Total number of cards = 52
All queen cards are removed. There are 4 queen cards in a deck.
Now, total number of cards = [tex]52-4[/tex]
⇒ [tex]48[/tex] cards.
The formula to find the selection by permutation is
[tex]nP_{r}=\frac{n!}{(n-r)!}[/tex]
Number of ways for unique four card combinations,
[tex]48P_{4}=\frac{48!}{(48-4)!}[/tex]
⇒ [tex]\frac{48!}{44!}[/tex]
⇒ [tex]\frac{(48)(47)(46)(45)44!}{44!}[/tex]
⇒ [tex](48)(47)(46)(45)[/tex]
⇒ [tex]4,669,920[/tex]
Hence we can conclude that the unique four card combinations in a deck of cards when all queens are removed is 4,669,920.
Learn more about permutations here
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