there are 24 balls of 6 different sizes in a bag there being 4 balls of each size in four different colours in how many ways 4 balls can be selected so that they are of different colours
Hello, prasum!
This one is very easy.
Exactly where is your difficulty?
$\displaystyle \text{There are 24 balls of 6 different sizes in a bag, there being 4 balls of each}$
$\displaystyle \text{size in four different colours. \:In how many ways 4 balls can be selected }$
$\displaystyle \text{so that they are of different colours?}$
Perhaps the idea of six sizes confused you.
This was only to show that the six red balls are distinguishable.
. . They could have been simply numbered: .$\displaystyle R_1,\:R_2,\:R_3,\:R_4,\:R_5,\:R_6$
There are 6 choices for a red ball.
There are 6 choices for a yellow ball.
There are 6 choices for a blue ball.
There are 6 choices for a green ball.
Therefore, there are: .$\displaystyle 6^4 = 1296$ ways.