Answer :
Answer: 0.339
Step-by-step explanation:
Given : Tour players Harry, Ron, Harmione and Ginny are playing a card game.
. A deck of 52 cards are dealt out equally.
Then, the number of card each person has = [tex]\dfrac{52}{4}=13[/tex]
If Harmione and Ginny have a total of 8 spades among them, then the total cards the total spades left = 13-8=5
Now, the number of ways to get 3 of 5 spades : [tex]^5C_3=\dfrac{5!}{3!2!}=10[/tex]
Number of ways to draw remaining 10 cards : [tex]^{21}C_{10}=\dfrac{21!}{10!11!}=352716[/tex]
Also, the total cards Harmione and Ginny have = 13+13=26
Then the total cards left = 26
The number of ways to get 13 cards for Harry :
[tex]^{26}C_{13}=\dfrac{26!}{13!(26-13)!}\\\\=\dfrac{26!}{13!13!}=10400600[/tex]
Now, the probability that Harry has 3 of the remaining 5 spades :_
[tex]\dfrac{^5C_3\times ^{21}C_{10}}{^{26}C_{13}}\\\\=\dfrac{10\times352716}{10400600}\\\\=0.339130434783\approx0.339[/tex]
Hence, the probability that Harry has 3 of the remaining 5 spades= 0.339 (approx)