There are two red, three blue, four white and K green socks in a drawer. If 2 socks are taken at random from the drawer without replacement, the probability that they are of the same colour is 1 5 , then K is equal to

Question

There are two red, three blue, four white and K green socks in a drawer. If 2 socks are taken at random from the drawer without replacement, the probability that they are of the same colour is 1 5 , then K is equal to,

MARKS App · Accepted Answer

Total cases = k + 9 C 2 Favourable cases = both are of same colour = C 2 2 + C 3 2 + C 4 2 + C k 2 So, 2 C 2 + 3 C 2 + 4 C 2 + k C 2 k + 9 C 2 = 1 5 ⇒ 10 + k k - 1 2 k + 9 k + 8 2 = 1 5 ⇒ 20 + k 2 - k k 2 + 17 k + 72 = 1 5 ⇒ 4 k 2 - 22 k + 28 = 0 ⇒ 2 k 2 - 11 k + 14 = 0 ⇒ k = 2 , 7 2 (rejected)

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