Statistics-The Martian language can be written with the familiar Roman alphabet

1. The Martian language can be written with the familiar Roman alphabet, which has 21 consonants (b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z) and 5 vowels (a, e, i, o, u). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, vux, diyok, and zobalut are possible Martian nouns, but x, vuv, diyik, zezelal are not. How many Martian nouns are possible? Briefly explain your answer.

2. Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian can be written with c consonants and vvowels, where c > v. Express the number of possible Martian nouns in terms of c and v.

3. We take two samples from two independent populations of sizes n1 = 30 and n2 = 35 respectively. The first population has a mean µ1 = 8 and variance σ21 = 1, and the second population has a mean µ2 = 7 and a variance σ22 = 5.

Find the probability that the sample means will differ by more than 0.5?