Compute the following using the inclusion-exclusion principle and Mbius inversion on posets. Recall that the poset you want to consider is the subset poset of the available properties, where you are trying to count instances that satisfy/dont satisfy certain properties. (a) Consider a standard 52-card deck. How many cards are there which neither belong to a red suit nor are a face card (that is, K, Q, or J)? (b) How many ways are there to rearrange the letters of the word "MOBIUS" so that the "M" is not in first place, "S" is not in last place, and the letters "BI" do not appear next to each other in that order?

Compute the following using the inclusion-exclusion principle and Mbius inversion on posets. Recall that the poset you want to consider is the subset poset of the available properties, where you are trying to count instances that satisfy/don't satisfy certain properties. (a) Consider a standard 52-card deck. How many cards are there which neither belong to a red suit nor are a face card (that is, K, Q, or J)? (b) How many ways are there to rearrange the letters of the word "MOBIUS" so that the "M" is not in first place, "S" is not in last place, and the letters "BI" do not appear next to each other in that order? Compute the following using the inclusion-exclusion principle and Mbius inversion on posets. Recall that the poset you want to consider is the subset poset of the available properties, where you are trying to count instances that satisfy/don't satisfy certain properties. (a) Consider a standard 52-card deck. How many cards are there which neither belong to a red suit nor are a face card (that is, K, Q, or J)? (b) How many ways are there to rearrange the letters of the word "MOBIUS" so that the "M" is not in first place, "S" is not in last place, and the letters "BI" do not appear next to each other in that order