In how many ways can seven friends be seated in a row at the theatre?

Question

BlackTom AI · Accepted Answer

The problem asks about seating seven distinct friends in a row.
First, consider that each seat is a position in a linear arrangement, and every friend is distinct, so we count permutations.
For the first seat there are 7 choices, for the second seat 6 choices (since one friend is already seated), for the third seat 5 choices, and so on, down to 1 choice for the last seat.
Multiplying these choices gives 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7!, which is a standard result for arranging n distinct items in a row.
Calculating 7! yields 5040, so the total number of seating arrangements is 5040.
In typical multiple-choice formatting, this count is commonly labeled as 7!, reflecting the factorial-based counting principle for permutations.
Note: If the answer options were missing or not displayed, the underlying concept remains the same: each of the seven friends must occupy a unique seat, and the number of distinct orders is the factorial of the number of people.

In how many ways can seven friends be seated in a row at the theatre?

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