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In how many different orders can you line up 6 cards on a table?

A. 120
B. 6
C. 1
D. 720

Sagot :

GinnyAnsweridn
To determine the number of different orders in which you can line up 6 cards on a table, we need to calculate the factorial of 6. The factorial of a number [tex]\( n \)[/tex] (denoted as [tex]\( n! \)[/tex]) is the product of all positive integers up to [tex]\( n \)[/tex].

Here's the step-by-step process to find [tex]\( 6! \)[/tex]:

1. Start with the number 6.
2. Multiply 6 by each descending integer until you reach 1:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \][/tex]

3. Perform the multiplications step-by-step:
- [tex]\( 6 \times 5 = 30 \)[/tex]
- [tex]\( 30 \times 4 = 120 \)[/tex]
- [tex]\( 120 \times 3 = 360 \)[/tex]
- [tex]\( 360 \times 2 = 720 \)[/tex]
- [tex]\( 720 \times 1 = 720 \)[/tex]

So, the number of different orders to line up 6 cards on a table is [tex]\( 720 \)[/tex].

Therefore, the correct answer is [tex]\( 720 \)[/tex].
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