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).

Question

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). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

( 5 C 1( 8 C 2-4)( 6 C 2-2)/ 10 C 2 ⋅ 8 C 2 ⋅ 6 C 2)=(26/315)=( m / n ) ∴ m =26 text and n =315 text Hence, n -12 m =315-312=3

10C2​⋅8C2​⋅6C2​5C1​(8C2​−4)(6C2​−2)​=31526​=nm​ ∴m=26 and n=315 Hence, n−12m=315−312=3

$\frac{^{5} C _{1} ( ^{8} C _{2} - 4 ) ( ^{6} C _{2} - 2 )}{^{10} C _{2} \cdot ^{8} C _{2} \cdot ^{6} C _{2}} = \frac{26}{315} = \frac{m}{n}$
$∴ m = 26 and n = 315$
$Hence, n - 12 m = 315 - 312 = 3$