The possible way to draw 5 cards hand from set of hearts-only deck is 15,4440 .
Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol [tex]P_{r} ^{n}[/tex] is used to denote the number of permutations of n distinct objects, taken r at a time.
Formula of permutation
[tex]P_{r} ^{n}[/tex] = [tex]\frac{(n!)}{(n-r)!}[/tex]
According to the question
Remove all of the hearts from a normal deck of cards.
i.e,
Total normal deck of cards = 52
On Removing hearts cards(n) = 13
Now, with this new hearts-only deck, how many possible five-card hands can you draw .
Card to draw (r)= 5
Applying formula of permutation
[tex]P_{r} ^{n}[/tex] = [tex]\frac{(n!)}{(n-r)!}[/tex]
n = 13
r = 5
Substituting the values
[tex]P_{r} ^{n}[/tex] = [tex]\frac{(13!)}{(13-5)!}[/tex]
[tex]P_{r} ^{n}[/tex] = [tex]\frac{(13*12*11*10*9*8!)}{(8)!}[/tex]
[tex]P_{r} ^{n}[/tex] = 15,4440
Hence, the possible way to draw 5 cards hand from set of hearts-only deck is 15,4440 .
To know more about permutation here:
https://brainly.com/question/1216161
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