I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(a) The candies are all different and the lunch boxes are all different?

(b) The candies are all the same and the lunch boxes are all the same?

(c) The candies are all the same and the lunch boxes are all different?

(d) The candies are all different and the lunch boxes are all the same?

(e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

Mr.Owl
Oct 22, 2017

#1**+2 **

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(a) The candies are all different and the lunch boxes are all different?

Melody
Oct 23, 2017

#2**+2 **

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(b) The candies are all the same and the lunch boxes are all the same?

The only difference is how many candies are in a lunch box

All in 1 1

2 in 1 and 1 in another 1

all in different boxes 1

3 ways

Melody
Oct 23, 2017

#3**+2 **

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(c) The candies are all the same and the lunch boxes are all different?

All in 1 4

2 in 1 and 1 in another 4*3=12

all in different boxes 4

4+12+4= 20 ways

Melody
Oct 23, 2017

#4**+2 **

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(d) The candies are all different and the lunch boxes are all the same?

All in 1 1

2 in 1 and 1 in another 3

all in different boxes (one box is empty) 1

5 ways

Melody
Oct 23, 2017

#5**+2 **

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

All in 1 4ways

2 the same in 1 box and the odd one in another 4*3=12

2 different in 1 box and the other in another 4*3=12

all in different boxes 4C2*2 = 6*2=12ways

4+12+12+12 = 40ways

Melody
Oct 23, 2017