2. During the first expedition to Mars, linguists discovered that the Martian la

Question

2. During the first expedition to Mars, linguists discovered that 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, grok, diyik, and zezelal are not. How many Martian nouns are possible? Your answer must be a number.

Explanation / Answer

There are total of 26 alphabets. First one must be a consonant. So, there are total of 21 ways to pick one.

The rest of the nouns must form vowel consonant pairs. There can be either 1 pair, 2 pairs, 3 pairs, 4 pairs or 5 pairs since only 5 vowels are present. So , total number of ways can be written as

ways = 21*((5)*(20) + (5*4)*(20*19) + (5*4*3)*(20*19*18) + (5*4*3*2)*(20*19*18*17) + (5*4*3*2*1)*(20*19*18*17*16))

= 21*(100 + 7600 + 410400 + 13953600 + 223257600) = 21*237629300 = 4990215300

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