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In a particular programming language a valid variable name can consist of a sequence of one to five alphanumeric characters A,B,C,D……..Z,0,1,2,……9 beginning with a letter. The number of valid variable name is

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$\frac{26}{35} (36^{5} - 1)$

$\frac{26}{35} (36^{5} + 1)$

$\frac{26}{25} (36^{5} - 1)$

$\frac{26}{25} (26^{5} + 1)$

answer is A.

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Detailed Solution

The first entry is a letter. The other entries are letters or digits,
so the desired number is $= \sum_{r = 0}^{4} 26 \times 36^{r}$
$= \frac{26}{35} (36^{5} - 1)$

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