Probability
# Permutations

How many 5 digit numbers can be formed if *either*

(a) every successive digit exceeds its predecessor,
*or*

(b) every successive digit is smaller than its predecessor.

Detail: Leading 0's don't count, aka 04521 is not a 5-digit number.

Alice, Benedict, Calvin, Dennis and Evelyn attended a party. At the end of the night, they each randomly grabbed a left shoe and a right shoe. What is the probability that each person left with exactly one of their own shoes?

Note: If the probability is 1%, enter it as 0.01.

$\huge INTERMEDIATE$ How many words can be made with the letters of the word $INTERMEDIATE$ if the order of vowels doesn't change ?

The "order of the vowels" refers to the sequence in which they occur. IE the sequence should be $I - E - E - I - A - E$.