Combinatorics

In how many different ways can we seat three people on three chairs, four on four, five on five, and six on six chairs?

Identify the common properties when arranging objects, from the perspective of combinatorics. Discover the principle for calculating all possibilities that satisfy the conditions in the task, and try to formulate a general formula.

Final Answer:

n₃ =  6
n₄ =  24
n₅ =  120
n₆ =  720

Step-by-step explanation:

$n_3=3\cdot 2\cdot 1=6$

$n_4=4\cdot 3\cdot 2\cdot 1=24$

$n_5=5\cdot 4\cdot 3\cdot 2\cdot 1=120$

$n_6=6\cdot n_5=6\cdot 120=720$

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