onetwothree = 0
fivesix = 0
seveneightnine = 0
rest = 0


perms = 1234567890.to_s.chars.to_a.permutation.map(&:join)

for i in perms
  if i.to_s =~ /^.......789$/ then seveneightnine += 1; next; end
  if i.to_s =~ /^.....56/ then fivesix += 1; next; end
  if i.to_s =~ /^123/ then onetwothree += 1; next; end
  #if i.to_s =~ /^.....56/ then fivesix += 1; next; end
  #if i.to_s =~ /^.......789$/ then seveneightnine += 1; next; end
  rest += 1
end

puts "onetwothree = #{onetwothree}; fivesix = #{fivesix}; seveneightnine = #{seveneightnine}; total =  #{onetwothree + fivesix + seveneightnine}"
puts "rest = #{rest}; total = #{rest + onetwothree + fivesix + seveneightnine}"
puts "perms.count = #{perms.count}"

# output:
# $ ruby perms2.rb
# onetwothree = 4898; fivesix = 40200; seveneightnine = 5040; total =  50138
# rest = 3578662; total = 3628800
# perms.count = 3628800