I’m a little confused as to when to calculate the possibility using factorial, raise to the...

I’m a little confused as to when to calculate the possibility using factorial, raise to the nth power and multiplication.

For example: roll a pair of 6-sided dice and there will be 36 outcomes. In this case I assume it’s 6*6 = 36

However, when should I use 6! or 6^6?

Thank you!

Expert Solution

Consider the same example of rolling a die. If you want to see all possible number of outcomes on n rolls, you use, 6ⁿ

That is, if rolled 2 times, number of outcomes = 6²

If rolled 5 times, number of outcomes = 6⁶

If you want to count the number of cases in which no letters can be repeated, number of possible outcomes = 6!

So, the basic difference is that when repetition is allowed, you use nth power and when repetition is not allowed, you use factorial.

A better example of a situation where you chose factorial is given below.

You have a list of 5 songs. You are interested in number of arrangements possible. The number of ways to arrange 5 songs = 5!

Here, we used factorial because songs are not repeated.

If A,B,C,D and E are the songs, then B,C,E,A,D is an arrangement of the song, but not B,C,B,B,E. In case of rolling a die, 3,2,5,1,6,4 and 3,2,5,2,5,5 is also a possible outcome and hence, we use nth power in that case.

orchestra answered 1 year ago

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