Solutions - 5070-09

(a)

Apply the permutation formula (letters first, digits last):

$$\begin{array}{c}{(26)}_5\cdot {(10)}_6=26\cdot 25\cdot 24\cdot 23\cdot 22\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\\ \\ \gg \gg \mathrm{1,193,512,320,000}\end{array}$$

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(b)

Multiply by the number of ways to interleave 5 letter positions and 6 digit positions:

$$\begin{array}{c}\left(\genfrac{}{}{0px}{}{11}{5}\right)\cdot {(26)}_5\cdot {(10)}_6\\ \\ \gg \gg 462\cdot \mathrm{1,193,512,320,000}\gg \gg \mathrm{551,402,691,840,000}\end{array}$$