Originally Posted by

**skhan** A general is planning to invade towns A, B, C and has 20 soldiers at his disposal (6 officers and 14 privates). After some thought, the general decides to select 12 soldiers to carry out the invasion and to keep the remaining 8 (and himself) behind to protect the command post. If the general takes 12 selected soldiers (3 officers and 9 privates), and randomly selects 4 soldiers w/o replacement, to invade towns A, B, C, what is the probability that exactly one officer ends up being sent to each town?

ANS: 0.2909

i dont think hes sending the same soldier again because in the original 12 he has 3 officers and 9 privares and then he choose 4 soldiers from the original 12 which could be offciers and/or privates...right?

The first part of the problem is irrelevent.

I understand the question like this, i think

There are 12 soldiers - 3 officers and 9 privates

The general randomly selectes 4 people and sents them.

Then from the remaining 8 he selects and he sents.

Then from the remaining 4 he sends them all.

The question is what is probability that an exactly one officer was sent to A or B or C.

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Try it like this,

write a box which shows all possible distributions of officers which is:

Code:

0 0 4
0 1 3
0 2 2
0 3 1
0 4 0
1 3 0
2 2 0
3 1 0
4 0 0
1 1 2
1 2 1
2 1 1

Which one(s) fit your question?