Answer:
1) n = 39916800
2) n = 1663200
3) n = 330
Step-by-step explanation:
1) If the blue balls are distinguishable as are the red balls
Then you can arrange these balls in the following ways, we must use a permutation
In totally we have 11 balls, then
n = 11P11
[tex]n = \frac{11!}{(11-11)!} = 11! = 39916800\\[/tex]
2) If Blue balls are distinguishable, but the red balls are identical
In this case, we need to do a correction due to the red balls are identical and we cannot identify the difference when we interchange two red balls
[tex]n = \frac{11!}{4!} = \frac{39916800}{24} = 1663200[/tex]
3) If the balls of each color are indistinguishable
We proceed equal to the before case but we include a correction due to blue balls also
[tex]n = \frac{11!}{4!*7!} = \frac{39916800}{24*5040} = 330[/tex]
