Answer
$a.\quad 27,600$
$b.\quad 35,152$
$c.\quad 1104$
Work Step by Step
Apply the Fundamental Principle of Counting
If $n$ independent events occur, with $m_{1}$ ways for event 1 to occur,
$m_{2}$ ways for event 2 to occur,
$\ldots$ and $m_{n}$ ways for event $n$ to occur,
then there are $m_{1}\cdot m_{2}\cdot\cdots\cdot m_{n}$ different ways for all $n$ events to occur.
---
$(a)$
$m_{1}=2 \qquad$ ... K or W
$m_{2}=25 \qquad$ ... one has been chosen, 25 letters remain
$m_{3}=24 \qquad$ ... two have been chosen, 24 letters remain
$m_{4}=23 \qquad$ ... three have been chosen, 23 letters remain
Total = $2\times 25\times 24\times 23$ = $27,600$
$(b)$
$m_{1}=2 \qquad$ ... K or W
$m_{2}=26 \qquad$ ... any letter
$m_{3}=26 \qquad$ ... any letter
$m_{4}=26 \qquad$ ... any letter
Total = $2\times 26^{3}$ = $35,152$
$(c)$
$m_{1}=2 \qquad$ ... K or W
$m_{2}=24 \qquad$ ... any letter, except the letter chosen first, and R
$m_{3}=23 \qquad$ ... any letter,\ except the letters chosen above, and R
$m_{4}=1 \qquad$ ... must be R
Total = $2\times 24\times 23\times 1$ = $1104$
