Chapter 4: Q1 (page 174)

Notation What does the symbol ! represent? Six different people can stand in a line 6! different ways, so what is the actual number of ways that six people can stand in a line?

Expert verified

The symbol “!” after any number represents the product of all non-zero positive integers equal to less than the given number.

The actual number of ways that six different people can stand in a line is equal to 720.

Step by step solution

The number of ways that six different people can stand in a line is equal to 6!.

The factorial of a number is the product of all the numbers (positive non-zero integers) equal or less than the given number up to 1.

It is represented by the symbol “!”.

Mathematically,

$n! = n \times (n - 1) \times . . . \times 1$

It is given that six different people can stand in a line in 6! ways.

The value of 6! is calculated as follows:

$6! = 6 \times (6 - 1) \times (6 - 2) \times . . . \times 1 = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$

Therefore, the number of ways that six different people can stand in a line is equal to 720.

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