Question

Suppose we have six $1 bills that we are going to hand out to 3 of...

Suppose we have six $1 bills that we are going to hand out to 3 of our friends. How many ways can we do that?

My teachers solution is 8 choose 2 using the but I thought the answer would be 3^6 since each dollar has the option of going to 3 different people.

Homework Answers

Answer #1

Since each dollar having option of going to 3 different people but each of 6 dollar are identical. If we would have 8 different objects which needs to be given to 3 people, your answer 36 was right. Here all the 6dollars are identical. So no of ways will be the no of non negative integral solution of the equation   

a+b+c = 6, where a b and c are no of dollars given to 3 friends.

which is C(6+3-1, 3-1) = C(8,2) = 28.

Since no of non negative integral solution of the equation

X1 + X2 + .....+ Xr = n is C(n+r-1, r-1)

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