In how many ways can the letters A, C, E, G, K, S be arranged

720

Step-by-step explanation:Now let's imagine we are filling them with letters. There are six places we can put the first letter, so after we've placed one letter, we have six different outcomes.

There are then five remaining gaps for the second letter, so we have 5*6=30 different outcomes after two letters.

There are four spaces for the third letter, three for the fourth letter, two for the fifth letter and finally we have to put the sixth letter in the remaining gap.

So we end up with 6*5*4*3*2*1=720 ways to arrange six different letters.

This is called the factorial function, and is denoted by an exclamation mark. The factorial function is defined as the number of ways to arrange n different options and is calculated as n! = 1*2*3*…*(n-1)*n, with a extra bit that 0!=1 as there is one way to arrange a set of 0 objects (this comes into play later in statistics).

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