Probability with 5 couples











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There are 5 couples. We need to make a team with 4 people. What is the probability that only one person from couple will be taken in the team?



I know that to take 4 people we can in $C^4_{10}=210$ ways. But I don't know how many ways we can choose 4 people that only one person from couple could be taken. Can somebody help me?






probability probability-theory







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    up vote
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    down vote

    favorite












    There are 5 couples. We need to make a team with 4 people. What is the probability that only one person from couple will be taken in the team?



    I know that to take 4 people we can in $C^4_{10}=210$ ways. But I don't know how many ways we can choose 4 people that only one person from couple could be taken. Can somebody help me?






    probability probability-theory







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      There are 5 couples. We need to make a team with 4 people. What is the probability that only one person from couple will be taken in the team?



      I know that to take 4 people we can in $C^4_{10}=210$ ways. But I don't know how many ways we can choose 4 people that only one person from couple could be taken. Can somebody help me?






      probability probability-theory







      share|cite|improve this question













      There are 5 couples. We need to make a team with 4 people. What is the probability that only one person from couple will be taken in the team?



      I know that to take 4 people we can in $C^4_{10}=210$ ways. But I don't know how many ways we can choose 4 people that only one person from couple could be taken. Can somebody help me?






      probability probability-theory




      probability probability-theory






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      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 2 hours ago









      Atstovas

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          First select the $4$ couples (out of $5$) that will provide in a team member.



          Then out of each of the $4$ selected couples select one person.



          There are $binom54binom21^4$ possibilities for this, leading to probability:$$frac{binom54binom21^4}{binom{10}4}$$






          share|cite|improve this answer





















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            First select the $4$ couples (out of $5$) that will provide in a team member.



            Then out of each of the $4$ selected couples select one person.



            There are $binom54binom21^4$ possibilities for this, leading to probability:$$frac{binom54binom21^4}{binom{10}4}$$






            share|cite|improve this answer

























              up vote
              1
              down vote













              First select the $4$ couples (out of $5$) that will provide in a team member.



              Then out of each of the $4$ selected couples select one person.



              There are $binom54binom21^4$ possibilities for this, leading to probability:$$frac{binom54binom21^4}{binom{10}4}$$






              share|cite|improve this answer























                up vote
                1
                down vote










                up vote
                1
                down vote









                First select the $4$ couples (out of $5$) that will provide in a team member.



                Then out of each of the $4$ selected couples select one person.



                There are $binom54binom21^4$ possibilities for this, leading to probability:$$frac{binom54binom21^4}{binom{10}4}$$






                share|cite|improve this answer












                First select the $4$ couples (out of $5$) that will provide in a team member.



                Then out of each of the $4$ selected couples select one person.



                There are $binom54binom21^4$ possibilities for this, leading to probability:$$frac{binom54binom21^4}{binom{10}4}$$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 2 hours ago









                drhab

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