Answer
20. MILLIMICRON contains 2 M’s, 3 I’s, 2 L’s, 1 C, 1 R, 1 O, 1 N
(■(A @ B)) = A choose B
a. (■(11@2))(■(9@3))(■(6@2))(■(4@1))(■(3@1))(■(2@1))(■(1@1))
= 11!/2!9! * 9!/3!6! * 6!/2!4! * 4!/1!3! * 3!/1!2! * 2!/1!1! * 1!/1!0!
= 5*11 * 7*4*3 * 5*3 * 4 * 3 * 2 * 1
= 11!/(2!3!2!1!1!1!1!)
= 1663200
b. (■(9@1))(■(8@3))(■(5@2))(■(3@1))(■(2@1))(■(1@1))
= 9!/1!8! * 8!/3!5! * 5!/2!3! * 3!/1!2! * 2!/1!1! * 1!/1!0!
= 9 * 7*8 * 2*5 * 3 * 2 * 1
= 9!/(1!3!2!1!1!1!)
= 30240
c. (■(9@2))(■(7@3))(■(4@2))(■(2@1))(■(1@1))
= 9!/2!7! * 7!/3!4! * 4!/2!2! * 2!/1!1! * 1
= 36 * 35 * 6 * 2
= 9!/2!3!2!1!1!
= 2*5*3*7*8*9
= 15120
Work Step by Step
20. MILLIMICRON contains 2 M’s, 3 I’s, 2 L’s, 1 C, 1 R, 1 O, 1 N
(■(A @ B)) = A choose B
a. (■(11@2))(■(9@3))(■(6@2))(■(4@1))(■(3@1))(■(2@1))(■(1@1))
= 11!/2!9! * 9!/3!6! * 6!/2!4! * 4!/1!3! * 3!/1!2! * 2!/1!1! * 1!/1!0!
= 5*11 * 7*4*3 * 5*3 * 4 * 3 * 2 * 1
= 11!/(2!3!2!1!1!1!1!)
= 1663200
b. (■(9@1))(■(8@3))(■(5@2))(■(3@1))(■(2@1))(■(1@1))
= 9!/1!8! * 8!/3!5! * 5!/2!3! * 3!/1!2! * 2!/1!1! * 1!/1!0!
= 9 * 7*8 * 2*5 * 3 * 2 * 1
= 9!/(1!3!2!1!1!1!)
= 30240
c. (■(9@2))(■(7@3))(■(4@2))(■(2@1))(■(1@1))
= 9!/2!7! * 7!/3!4! * 4!/2!2! * 2!/1!1! * 1
= 36 * 35 * 6 * 2
= 9!/2!3!2!1!1!
= 2*5*3*7*8*9
= 15120