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...