I think it should be b'misrad. The definite article should be on the last word only (theסומך) in the construct chain. When you have it bamisrad, you're having "the" twice (in the first word [the נסמך] and the last word).
It said I have a typo because I selected Minister and then 's to say "Minister's." It corrected me and said the correct way is to say "Minister s" - with no apostrophe. That is wrong, and it had not even been an option. I HAD NO TYPO!!!! I'm OK. :)