A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :

 

  • Option 1)

    28

  • Option 2)

    27

  • Option 3)

    25

  • Option 4)

    24

 

Answers (1)

atleast one boy & one girl : 

( 1B & 2G) + ( 2B & 1G)

_{1}^{5}C\textrm{}._{2}^{n}C\textrm{}+_{2}^{5}C\textrm{}._{1}^{n}C\textrm{}=1750

=> 5 \frac{n(n-1)}{2}+10.n=1750

 => \frac{n(n-1)}{2}+2.n=350

=> n^{2}-n+4n=700

=> n^{2}+3n-700=0

=> (n+28)(n-25)=0

=> n=25,-28

As, n cannot be -ve so, n = 25


Option 1)

28

Option 2)

27

Option 3)

25

Option 4)

24

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