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# Need clarity, kindly explain! 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, i

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

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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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