permutation combination

The digits 4, 4, 5, 5, 6, 6 are permuted to form a six-digit number.
a) How many different six-digit numbers can be formed?
b) How many of them have at least one pair of consecutive digits equal?


a)
(For 6 different digits to form a 6-digit number, total number of permutation =6P6)
(Interchange of the two "4", two "5", or two "6",it will give the same 6-digits.")
(Thus, the number of permutation should be divided by 2*2*2.)

Number of 6-digit numbers that can be formed
= 6P6 / (2*2*2)
= 6! / 8
= 720 / 8
= 90

b)
(Consider that the 6-digit number without any consecutive digits equal.)
(Firstly, choose a pair of "4", "5" or "6" (3C1)and arrange them as _X_X_.)
(Secondly, choose a pair from the rest 2 pairs (2C1), andfill them in two "_" in above (3C2).)
(Then, it looks as _X_X_X_X_.)
(Thirdly, fill the last pair of digits into two "_" in above (5C2).)
(Finally, divide by the number of repetition (3P3).)

Number of 6-digit numbers having at least one pair of consecutive digits equal
= 90 - (Number of 6-digit numbers without any pair of consecutive digits equal)
= 90 - (3C1 * 2C1­ * 3C2* 5C2 / 3P3)
= 90 - (3 * 2 * 3 * 10 / 6)
= 90 - 30
= 60

Ans of b) = 438?