<p>A machine is used to generate codes consisting of $4$ characters. A character is either one of the $26$ letters of the alphabet A-Z or one of the $10$ digits $0$-$9$. Each of the $36$ characters are equally likely to be generated and each character can be generated more than once.</p>
<p>Find the number of codes generated by the machine with</p>
<ol class="i-list"><li><div class="list-item-paragraph">no digits,	<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">the first two characters consisting of digits and the first digit is higher than the second digit,<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">three different letters and one digit,		<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">exactly two letters and two digits, such that the letters are the same or the digits are the same, but not both<span class="inline-marks">[3]</span></div></li></ol>

A machine is used to generate codes consisting of $4$ characters. A character is either one of the $26$ letters of the alphabet A-Z or one of the $10$ digits $0$-$9$. Each of the $36$ characters are equally likely to be generated and each character can be generated more than once.

Find the number of codes generated by the machine with

the first two characters consisting of digits and the first digit is higher than the second digit,

exactly two letters and two digits, such that the letters are the same or the digits are the same, but not both

2014 MI P2 Q11 [Modified]

2014 MI P2 Q11 [Modified]

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