Latest self Aptitude Question SOLUTION: There are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.

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There are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.

Solution

First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 8
and for second = 7
so total methods = 8*7 = 56

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karthik (13 years ago)

Solved Read Solution (7)

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Garima  (13 years ago)

7 pairs can be formed.

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Pargat Pal Singh  (13 years ago)

one sock of first pair can form 7 pairs with one sock of other pairs.
one sock of second pair can form additional 6 pairs with one sock of other pairs except first pair..
...
..
one sock of 7th pair can form additional 1 pair with one sock of 8th pair..

so total
7+6+5+4+3+2+1 = 28 pairs can be formed.

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kewal  (13 years ago)

In case of socks where left and right socks of a pair are different, only then 56 pairs are possible.
But normally socks of a pair are not different, so 28 pairs are possible.

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Pargat Pal Singh  (13 years ago)

7 such pairs can be formed so that the pair of socks worn are not of the same pair.

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karthik  (13 years ago)

This puzzle is given by me.......for that question given answer is 56 But how to come i dont know please explain me

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Rakesh Kumar Kohli  (13 years ago)

There are 8 pair of socks which means there are 16 socks.
We can choose two socks from sixteen socks in 16C2 ways = 16*15/2 = 120 ways two make pairs of socks. Of these only 8 matching pairs. Remaining 112 ways are not making matching pairs. But as each pair has two socks of the same type, so in fact there will be two unmatching pairs of each type. Thus there are will be 112/2 = 56 different unmatching pairs.

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abhishek   (13 years ago)

the solution is 28*2=56 becoz for one sock from
pair one sock of first pair can form 7 pairs with one sock of other pairs.
one sock of second pair can form additional 6 pairs with one sock of other pairs except first pair..
...
..
one sock of 7th pair can form additional 1 pair with one sock of 8th pair..

so total
7+6+5+4+3+2+1 = 28 pairs can be formed.

and this will be applied for second sock of all pairs
hence 28*2=56

alternately by permutation law nPr=n!/(n-r)!
put n=8 and r=2

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