Question

There are 5 Red, 4 White and 3 Greta marbles in a bag. If all are drawn, determine the number of different arrangemetts.

Answer 1

Answer:

27720

Step-by-step explanation:

Hi,

Given that there are 5 Red marble, 4 white marbles and 3 green

marbles.

Assuming all 5 Red marbles are identical to each other

Assuming all 4 White marbles are identical to each other

Assuming all 3 Green marbles are identical to each other

If all these are drawn one after one from the bag and arranged,

Since there are 12 marbles in total all of these can be arranged

in 12! ways, but since 5 identical red marbles can be permuted

between themselves in 5! ways giving rise to same

arrangement, we need to divide by 5!,

Also  since 4 identical white  marbles can be permuted between

themselves in 4! ways giving rise to same arrangement, we

need to divide by 4!

Since 3 identical Green marbles can be permuted between

themselves in 3! ways giving rise to same arrangement, we

need to divide by 3!,

So, different number of arrangements are 12!/5!4!3!

= 27720

Hope, it helps !