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?

Find common properties when selecting objects from the point of view of combinatorics. Find out the principle of calculating all possibilities that meet the conditions in the task assignment and try to formulate a general relationship for their calculation.

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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