how many different ways can 2 balls be drawn from a bag containing 5 balls? each ball is a different color, and first ball is replaced before the second one is selected. also how many ways are there if the ball is not replaced?

Question

kropot72 · Answer

The number of permutations of n different things taken k at a time with repetitions is:
$$n ^{k}=5^{2}=you\ can\ calculate$$
The number of permutations of n different things taken k at a time without repetitions is:
$$\frac{n!}{(n-k)!}=\frac{5!}{(5-2)!}=you\ can\ calculate$$

ybarrap · Answer

Case 1

A. How many ways can you pick the 1st ball: 5 ways
B. Put the ball back in the bag
C. How many ways can you pick the 2nd ball: 5 ways

The number of ways of doing A and C is 5*5=25

Case 2

A. How many ways can you pick the 1st ball: 5 ways
B. DON'T put the ball back in the bag
C. How many ways can you pick the 2nd ball: 4 ways

The number of ways of doing A and C is 5*4=20

Once you understand the concept, you can move to formulas to make the calculations easier.