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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?

 Nov 13, 2022
 #1
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What is the probability that three cards have the same number?

Descriptive solution below:

 Nov 13, 2022
 #2
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Solution:

 

Description:

Choose one (1) of the seven (7) numbers, then choose three (3) of the four (4) colors for these numbers.

Then choose one (1) of six (6) numbers and then choose one (1) of the four (4) colors for this number.

Then choose one (1) of six (6) numbers (again), and then choose one (1) of the four (4) colors for this number (again).

 

Then divide this by the \(\dbinom {27}{5}\)ways to choose a set of five (5) card from a population of 27 cards. 

 

Descriptive Math:

 

\(\dfrac { \dbinom {7}{1} * \dbinom {4}{3} * \dbinom {6}{1} * \dbinom {4}{1} * \dbinom {6}{1} * \dbinom {4}{1}} {\dbinom {27}{5} } = \Large 896/4485 \leftarrow \text {exact probability}\)

 

GA

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GingerAle  Nov 13, 2022

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