A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to

Options

A. `(12!)/(6!6!6^(12))`
B. `(2^(12))/(2^(6)6^(12))`
C. `(12!)/(2^(6)6^(12))`
D. `(12!)/(6^(2)6^(12))`

Answer

C

Explanation

Required probability
`= .^(12)C_(2)xx .^(10)C_(2)xx .^(8)C_(2)xx .^(6)C_(2)xx .^(4)C_(2)xx .^(2)C_(2)xx ((1)/(6))^(12)`
`=(12!)/(10!xx2!)xx(10!)/(8!xx2!)xx(8!)/(6!xx2!)xx(6!)/(4!xx2!)xx(4!)/(2!xx2!)xx(2!)/(2!xx0!)xx((1)/(6))^(12)=(12!)/(2^(6)xx6^(12))`