Question

Out of the letters $A,B,C,p,q,r$ how many arrangements can be made (1) beginning with a capital, (2) beginning and ending with a capital?

Answer 1

$\left(1\right)+-----$
$A,B,\overline{C}$
Let place can be filled in $3$ ways, and all the rest $5$ place can be in $5!$ ways.
$\therefore$ Total $=3\times 5!$
$=360.$

$\left(2\right)+----+$
$A,\overline{B},C$ $A,\overline{B},C$
Let place and last place can be filled in $3$ and $2$ ways respectively, and the rest in $4!$ ways
$\therefore$ Total $=3\times 4!\times 2$
$=144$