Binominal Coefficent

Mathematical Foundations (Discrete Structures)

Instructions Complete the following problems by filling in the blanks. Short blanks (^') permit single characters (e.g., 2) or complex characters representing arithmetic operations (e.g., 5, 5', V5, 65!), but not strings (e.g., {0}" is a string comprised of the characters '{', '0', and *}'); while long blanks ( permit strings (i.e., an ordered set of one or more characters). Amounts should be represented with the fewest characters or most legible format possible (e.g., use (15) instead of 1365, but use 10 in lieu of ()). How many length-5 binary strings contain exactly two ls? How many length-5 ternary strings over {0, 1, 2} contain exactly two 2s? Let S C Z with |SI = n. What is the maximum value of |{a+b: a,b E S Aa #b}|