Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects

total shoes 12
ways to select 2 pink: 4*3=12
total possibilities: 12*11
So final solution: 12/(12*11) = 1/11

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Anyone else want to try?
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Why D?
6 pairs = 12 shoes
C(4,2) / C (12 / 2) = 1 / 11

Bunuel Although I solved the problem as others have done it, upon carefully reading the problem statement I observed that the question mentions different pairs and matching pair.
So I tried to break the problem as below:

Total shoes: 12(6 pairs)

Step 1: there are 4 possibilities to pick a pink shoe.
So 4/12

Step 2: now the probability that the second shoe picked is pink and a match to the first picked shoe is 1/11 ( without replacement we have 11 shoes remaining) but there is only 1 out of those which will be a match.
So the answer is: 1/33

PS: had the question not mentioned different pairs and matching pair, 1/11 would have been correct.


Not sure if my analysis is correct. But I tried to reverse engineer from the answer to the steps.

Posted from my mobile device

Sigh like with all the Probability and combination questions the answer seems so obvious after youve got it wrong once .

Got it wrong on the first try picked C

2nd try -

Total no of shoes = 6* 2 = 12
No of pink shoes = 2*2 = 4

Probability of picking a matching pair = prob of picking a pink shoe * Prob of picking the shoe that forms the pair for picked shoe
= 4/12 * 1/11 (as only one of the remaing 11 will form a pair with the first shoe)
= 1/33

6 pairs = 12 shoes
select one pink shoe = 4/12 = 1/3
selecting its matching pink shoe = 1/11 (since we need to make matching pair)


probability of selecting this pair = 1/3*1/11 = 1/33

Given: Harry has 6 different pairs of shoes, 2 pairs are pink.
Asked: If he selects 2 individual shoes at random and without replacement, what is the probability that he selects a matching pink pair ?

Total shoes = 6*2 = 12
Pink shoes pairs = 2

The probability that he selects a matching pink pair = 2C1/12C2 = 2/66 = 1/33

IMO D
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There are 6 pairs, two are pink but each pair is distinct.
This means that we have 12 shoes out of which 4 are pink - Pink1Left, Pink1Right, Pink2Left, Pink2Right

We need to select a matching pink pair which means we need to select either {Pink1Left, Pink1Right} or {Pink2Left, Pink2Right}.

For our first pick, we can pick any one of the 4 pink shoes with the probability 4/12 = 1/3 (say we picked up Pink1Right)

For our second pick, we must now pick only Pink1Left. There is only 1 way to correctly make a matching pink pair out of the leftover 11 shoes now. So probability = 1/11

Total Probability of picking a matching pink pair = (1/3) * (1/11) = 1/33

Answer (D)
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Total possible selections = \(^{12}C_2\) = 66

Number of favorable outcomes = 2 (i.e. one for each pair)

Required Probability = \(\frac{2}{66}\) = \(\frac{1}{33}\)

Option D
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