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

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- Jan 20th 2011, 04:42 AMprasumcombination
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

- Jan 20th 2011, 06:11 AMSoroban
Hello, prasum!

This one is very easy.

Exactly where is your difficulty?

Quote:

$\displaystyle \text{There are 24 balls of 6 different sizes in a bag, there being 4 balls of each}$

$\displaystyle \text{size in four different colours. \:In how many ways 4 balls can be selected }$

$\displaystyle \text{so that they are of different colours?}$

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.