Need the following assignment Consider lists made from the l

Need the following assignment:

Consider lists made from the letters T, H, E, O, R, Y, with repetition allowed. How many length-4 lists are there? How many length-4 lists are there that begin with T? How many length-4 lists are there that do not begin with T? Airports are identified with 3-letter codes. For example, the Richmond, Virginia airport has the code RIC, and Portland, Oregon has PDX. How many different 3-letter codes are possible? Five cards are dealt off of a standard 52-card deck and lined up in a row. How-many such line-ups are there in which all 5 cards are of the same suit? Five cards are dealt off of a standard 52-card deck and lined up in a row. How-many such line-ups are there in which exactly one of the 5 cards is a queen?

Solution

1) a) 6 letters are their, 4 length=>6c₄=30

b) Starts with T => first place is fixed. remaining 3 places we have 5 letters remaining=>5c₃=20

c) Does not starts with T=> total-starts with=>30-20=10

2) 4-> 1. first 3 letters 2. 1st, middle, last. 3) first, last 2 4) first and any 2

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