Dennis03 wrote:

in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

1) 20

2) 24

3) 120

4) 625

5) 1024

I saw this question on a youtube video and the solution showed 4*4*4*4*4 = 1024, but i was thinking it would be 5*5*5*5 and this answer isn't even in the options. Please help me understand this.

Let the 5 cholcolates be : \(C_1\) , \(C_2\) , \(C_3\) , \(C_4\) & \(C_5\)

And there be 4 Students : \(S_1\) , \(S_2\), \(S_3\) & \(S_4\)

Now, The first Chocolate can be given in 4 ways ( Either to \(S_1\) or \(S_2\) or \(S_3\) or \(S_4\) )

The Second Chocolate can be given in 4 ways ( Either to \(S_1\) or \(S_2\) or \(S_3\) or \(S_4\) )

The Third Chocolate can be given in 4 ways ( Either to \(S_1\) or \(S_2\) or \(S_3\) or \(S_4\) )

The Fourth Chocolate can be given in 4 ways ( Either to \(S_1\) or \(S_2\) or \(S_3\) or \(S_4\) )

The fifth Chocolate can be given in 4 ways ( Either to \(S_1\) or \(S_2\) or \(S_3\) or \(S_4\) )

Hence, the total No of ways possible is \(4^5\) = \(1024\)

Hence, answer will be (E) 1024...