Ask Experts Questions for FREE Help !
Ask
    MRBEE's Avatar
    MRBEE Posts: 3, Reputation: 1
    New Member
    		  
    #1

    Apr 2, 2008, 04:10 PM
    probability of being seated together
    Three married couples are to be randomly seated around a circular table. What is the probability that at least one of the couples will be seated next to one another?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #2

    Apr 2, 2008, 06:16 PM
    When seating in a circular permutations, there are (n-1)! Ways to do so without restriction.

    In this case, 5!=120 ways to seat the 3 couples(6 people) without restriction.

    The opposite of 'at least one' is none. So, find the probability of no couples sitting together

    and subtract from 1. Or find the number of ways 1 couple can sit together, 2 couples, and

    three couples can sit together and add them up.

    For two couples together, we can choose 2 pairs in C(3,2)=3 ways and this pair can be

    arranged in 2 ways. The next pair in 2 ways and the next pair in two ways.

    So, we have ways for two couples to be seated together.

    Following the same logic, there are ways for 1 couple to be

    seated together and ways for all three to be seated together.

    Therefore, we have 16+24+48=88 ways for at least one couple to be seated together.

    The probability would be 88/120=11/15.
Not your question? Ask your question View similar questions
 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Probability [ 3 Answers ]

The Master Card center of a bank in Calgary has found that 62 percent of cardholders pay their new monhly balance in full before the payment due date. Suppose the credit center selects four cardholders at random. Use this information to answer the following questions. a) What is the...

Probability help [ 4 Answers ]

What are the odds of choosing two clubs out of a deck of 52 cards?

Probability [ 2 Answers ]

a.) when rolling three dice, what is the probability of rolling at least one 1? b.) when rolling three dice, what is the probability of rolling exactly one 1?

Probability [ 5 Answers ]

I need help with these questions, I just can't seem to get them right. 1. Separate the 12 face cards from the rest of the deck. Assume that the remaining cards have been shuffled. Select THREE cards from the pile of face cards (i.e. 3 jacks, 3 queens, or 3 kings) from the pile? 2....

Probability [ 5 Answers ]

If You Flip A Coin And Toss A 1-6 Number Cube, What Is The Probability Of Choosing A Prime Number And Tails.

View more questions Search