Discrete Math about Combinatorics.

(1) How many solutions over the positive integers are there to the inequality: X1 + x2 + ... + X10 $ 100 (2) Answer the following questions with a number or a simple formula involving factorials and binomial coefficients. Briefly explain your answers. (a) How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? Hint: Every vowel appears to the left of a consonant. (b) How many ways are there to order the 26 letters of the alphabet so that there are at least two consonants immediately following each vowel