There are ten pairs of socks in a cupboard from where 4 indiviual socks are picked at random.The prob that there is at least one pair is -
a) 195/323
b) 99/323
c) 198/323
d) 185/323
Thought process-
I think that the probability of atleast one pair = (1 - probability of matching no pair)
so I proceeded as follows -
4 socks are drawn in 20 C 4 ways.
therefore n(s) = 20C4
Now let us say
Ist Row - 1 2 3 4 5 6 7 8 9 10
2nd Row 1' 2' 3' 4' 5' 6' 7' 8' 9' 10'
1st socks can be selected in 20 C 1 let say 1 from Ist row.
2nd sock must not be the 1' therefore it can selected from remaining 18 socks in
18 C 1 ways = 18 let say it is any socks like 6.
3rd sock must not be 1' as well as 6' therefore It can be drwn from the remaining 16 balls. let say it is 10.
similarly 4th ball is drawn in 14 ways
probability of not matching even a single pair is
1 - (20 . 18 . 16 . 14 )/20C4.
Please guide me If I am on right way or missing out something.
Also the book answer for this is 99/323.
Anshu.