if we pick two gloves at random from a drawer containing nin

if we pick two gloves at random from a drawer containing nine different pairs of gloves, what is the probability :(a) the two chosen are a right-hand and a left-hand but do not form a pair?

(b) both are right hands ?

(c) a pair is chosen?

Solution

There are 18C2 = 153 ways to choose any 2 gloves.

a)

Ther are 9 ways to choose a right hand and 9 ways to choose a left, hence, 9*9 = 81 ways to choose a right and left hand.

However, there are 9 proper pairs.

So, there are 81 - 9 = 72 such non-pairs.

Thus,

P = 72/153 = 8/17 [ANSWER]

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b)

There are 9C2 = 36 ways to choose 2 right hands. Thus,

P = 36/153 = 4/17 [ANSWER]

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c)

There are 9 pairs, so

P = 9/153 = 1/17 [ANSWER]