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**NineZeroFive** 1) Fran is working on a word puzzle and is looking for four-digit "scrambles" from the clue word *calculate*.

a) How many of the possible four-letter scrambles contain four different letters?

b) How many contain two a's and one other pair of identical letters?

c) How many scrambles consist of any two pairs of identical letters?

d) What possiblities have you not yet taken into account? Find the number of scrambles for each of these cases.

e) What is the total number of four-letter scrambels taking all cases into account?

2) How many numbers can be formed using all of the digits 1, 2, 3, 4, 5, 6, and 7 if the odd digits must be in ascending order and the even digits in descending order?