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In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck are shown below.

 

Yunseol draws 5 cards from Ms. Q's deck. What is the probability that three cards have the same number?

 Mar 23, 2023
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I think this is from Beast Academy (Ms. Q)

 

After picking the 1st one, there are 27 left. And there are 3 of the same number as on the first one. So \frac{3}{27} = \frac{1}{9}

After that, there are 26 left. And there are 2 of the same number left, assuming that the first 2 matched. So, it is \frac{3}{26} * \frac{1}{9} = \frac{3}{234} = \boxed{\frac{1}{78}}

First answer on this site ūü•≥

btw, how to you get the LaTeX code to work?

 Mar 23, 2023
edited by Guest  Mar 23, 2023
edited by Guest  Mar 23, 2023
edited by Guest  Mar 23, 2023
edited by Guest  Mar 23, 2023

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