Question

Sean is arranging 4 decorations on fireplace mantel. How many arrangements are possible?

Answer 1

\(4!\)

Answer 2

in other words \(4\times 3\times 2\)

Answer 3

how did you get 3x2

Answer 4

4! = 4x3x2x1

Answer 5

ikr^ idont get it lol

Answer 6

you have 4 decorations, lets call them A, B, C and D and you are going to arrange them in some order on your mantel. lets make the slots

____ ____ ____ _____
so one possibility could be

A C B D
____ ____ ____ ____

Answer 7

question is how many ways are there to do this?
first pick one to go in the first slot
you have 4 choices
now pick one to go in the second slot
you have 3 choices (since one has been chosen)
then pick one to go in the third slot
you have 2 choices (since two have been chosen)
now you have no choices for the last slot since you have placed the other 3 already


by the counting principle, the number of ways to do all these together is the product of the number of ways to do them individually, so it is
\[4\times 3\times 2=24\]

Answer 8

so the answer is 24?
not 4

Answer 9

the answer is 24 and \(4!\) does not mean really really it is 4, \(4!\) is short notation for
\[4\times 3\times 2\] and is called 4 "factorial"

Answer 10

for example \[6!=6\times 5\times 4\times 3\times 2\]

Answer 11

oh my gosh . I'm only in 7th grade and I don't understand this lol

Answer 12

so what should I put on the answer slot lol

Answer 13

yes of course if you have not seen it before you do not understand it, but i hope it is clearer now
counting principle says if there are 5 ways to do one thing and 3 ways to do another, then there are 15 ways to do them together

more generally if there are n ways to do one thing and m ways to do another then there are \(m\times n \) ways to do the two tasks together

Answer 14

the answer is 24
the equation is 4! which is = to 4x3x2x1 and that multiplies out to 24