Online Course Discussion Forum

MC I-A Counting and Probability Homework 4.20

 
 
Picture of Tiger Chai
MC I-A Counting and Probability Homework 4.20
by Tiger Chai - Thursday, July 8, 2021, 10:30 AM
 

Hi, Could you explain how to solve homework 4.20 in MC I-A Counting and Probability?

"How many total ways can you draw red cards and black cards from a standard deck of cards so that theblack cards appear consecutively in the card draw?"

 
Picture of Areteem Professor
Re: MC I-A Counting and Probability Homework 4.20
by Areteem Professor - Monday, July 12, 2021, 2:23 PM
 

There are four ways to grab the $5$ cards so that the $2$ black are consecutive: $BBRRR$, $RBBRR$, $RRBBR$, and $RRRBB$.

There are $26 \times 25 \times 26 \times 25 \times 24 = 10140000$ ways to grab the cards precisely in $BBRRR$ order. You can find the number of ways to grab the cards in the other three cases in a similar way.