# permutation problem 4

• Apr 26th 2009, 06:01 AM
wheresthecake
permutation problem 4
hey guys, need some help with this problem. this is one of four permutation problems that our teacher gave us to solve but haven't really figured it out, plus i was sick so i missed the lecture..

4) 3 balls are to be drawn one at a time from an urn containing 8 distinct ones. Find the number of ways these 3 balls can be drawn if a) a drawn ball has to be replaced before drawing the next and b) there is no replacement of drawn balls.

thanks for the help. we've been given all the basic formula for permutations but I'm at a loss at how to apply them still.
• Apr 26th 2009, 09:18 PM
SengNee
Quote:

Originally Posted by wheresthecake
hey guys, need some help with this problem. this is one of four permutation problems that our teacher gave us to solve but haven't really figured it out, plus i was sick so i missed the lecture..

4) 3 balls are to be drawn one at a time from an urn containing 8 distinct ones. Find the number of ways these 3 balls can be drawn if a) a drawn ball has to be replaced before drawing the next and b) there is no replacement of drawn balls.

thanks for the help. we've been given all the basic formula for permutations but I'm at a loss at how to apply them still.

Logically, we drawn the ball one by one.

With replacement:
1st draw: 8 distinct balls in the urn
2nd draw: 8 distinct balls in the urn as the previous drawn ball is replaced into the urn.
3rd draw: 8 distinct balls in the urn as the previous drawn ball is replaced into the urn.
$^8P_1 \cdot ^8P_1 \cdot ^8P_1$

No replacement:
1st draw: 8 distinct balls in the urn
2nd draw: 7 distinct balls in the urn as the previous drawn ball is not replaced into the urn and now outside the urn.
3rd draw: 6 distinct balls in the urn as the previous drawn ball is not replaced into the urn and now outside the urn.