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Sagot :
By using the principle of counting, it can be calculated that
Total number of ways to arrange the four face cards in a 52-card deck = 11880
What is principle of counting?
Principle of counting states that if there are m ways to do one job and m ways to do another job after that job, there are m [tex]\times[/tex] n ways to do both the jobs together.
There are three face cards of hearts, three face cards of diamonds, three face card of clubs and three face cards of spade
Total number of face cards = 3 + 3 + 3 + 3 = 12
We can arrange the four face card in [tex]{12 \choose 4}[/tex] ways = 495 ways
The four cards should be arranged in a row.
Number of choices for the first card = 4
Number of choices for the second card = 3
Number of choices for the third card = 2
Number of choices for the fourth card = 1
Total number of ways to arrange the four cards in a row = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 24
Total number of ways to arrange the four face cards in a 52-card deck =
495 [tex]\times[/tex] 24 = 11880
To learn more about principle of counting, refer to the link-
https://brainly.com/question/16858325
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