Answer:
660 ways
Step-by-step explanation:
we have two numbers in consecutive positions in this question
(1,1) and (2,2)
numbers of ways that (1,1) are in consecutive positions = 6!/2! = 360
number of ways that (2,2) are in consecutive positions = 6!/2! = 360
the permutation of (11),(22),3,4,5 = 5!
ps: I counted the pairs as one each.
5! = 120
to get total number of permutations
7!/2!2!
= 5040/4
= 1260
the number of ways that 2 identical digits are not consecutively positioned = 1260-360-360+120
= 660 ways
