1. Tardigrade
  2. Question
  3. Mathematics
  4. Adrawer contains 5 pairs of socks, each pair is of different colour. On monday Mr. Aselects 2 individual socks at random from the 10 socks in the drawer. On tuesday Mr.A selects 2 of the remaining 8 socks at random and On wednesday 2 of the remaining 6 socks at random. The probability that wednesday is the first day Mr.A selects matching socks is ((m/n)) where m, n are coprime. Find the value of (n-12 m).

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Q. Adrawer contains 5 pairs of socks, each pair is of different colour. On monday Mr. Aselects 2 individual socks at random from the 10 socks in the drawer. On tuesday Mr.A selects 2 of the remaining 8 socks at random and On wednesday 2 of the remaining 6 socks at random. The probability that wednesday is the first day Mr.A selects matching socks is $\left(\frac{m}{n}\right)$ where $m$, $n$ are coprime. Find the value of $(n-12 m)$.

Probability - Part 2

Solution:

$\frac{{ }^5 C _1\left({ }^8 C _2-4\right)\left({ }^6 C _2-2\right)}{{ }^{10} C _2 \cdot{ }^8 C _2 \cdot{ }^6 C _2}=\frac{26}{315}=\frac{ m }{ n }$
$\therefore m =26 \text { and } n =315$
$\text { Hence, } n -12 m =315-312=3 $