Question

k people get off a plane and walk into a hall where they are assigned to at most n queues. The number of ways in which this can be done is

Answer 1

1 person can take one out of n queues

Therefore k people can take kn number offways

Therefore answer is kn

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Answer 2

Answer:

n(n+1)...(n+k-1)

Step-by-step explanation:

To divide k people into n queues, n-1 bars will be needed. Since after the first person selects a queue, n-1 queues are left.

At most n queues indicates that there could be some queues that have no one standing.

Therefore, (k+n-1)c(n-1) ways are there to way these n-1 bars.

Since these people could be permuted,

we get (k+n-1)c(n-1)×k!

Solving this, we get: n(n+1)...(n+k-1)