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There are two red, two blue, two white and certain number (greater than 0) of green socks Ln a drawer. If two socks are taken at random from the drawer without replacement, the probability that they are of the same colour is 1/5 then the number of green socks is-'

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answer is 4.

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Detailed Solution

Let the number of green socks are x > 0 E : two socks drawn are of the same color ⇒P(E)=P(RR or BB or WW or GG)=3C2 6+x+C2 xC2 6+x =6(x+6)(x+5)+x(x−1)(x+6)(x+5) =15( given )⇒5x2−x+6=x2+11x+30⇒4x2−16x=0⇒ x=4

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