This is a very basic self learning question, the scenario is there are 36 cards of 4 suits from 1 to 9 of each suit. One can pick a hand of 9 cards. My question is how many ways can someone pick a hand which contains all the 1's given that:
1) the order of the cards in the hand doesn't matter. Initially I thought this would be 36! /(4! X 5! X 27!) - from the concept of arranging among the 36 cards that 4 always chosen 1's, 5 selected and 27 non-selected out of the 36, but it turns out to be combination(32,5) as 4 1's are always chosen and we are left to choose the rest 5 from the 32 cards. I get this explanation but what am I doing wrong with my arranging approach stated formerly?
2) the order of the cards in the hand matter. Kind of lost on this one.