jack has flags for 4 different football teams. he wants to hang the flags in a straight line on his bedroom wall. in how many different ways could jack hang the 4 flags?
I came up with 16. 4*4=16
But 16 is not in the answer choice.
Answer choices are- 24,12,8,4
My second guess on 24. I don’t know how to get 24.
Plz help. Thank you
Let's experiment. We'll call the flags A, B, C, D.
A B C D
A B D C
A C D B
A C B D
A D B C
A D C B
Keep going
The first place can be filled by 4 different flags,
leaving 3 flags that go go in the second spot,
leaving 2 flags that can go in the third spot,
leaving you with 1 flag for the last spot,
so, the number of ways = 4*3*2*1 = 4! = 24
To find the number of different ways Jack can hang the 4 flags, we need to consider the concept of permutations.
In this case, since the flags are arranged in a straight line, order matters. Let's break down the problem step by step:
First, Jack has 4 options for choosing the flag to hang on the first position. Then, he has 3 remaining options for choosing the flag to hang on the second position.
For the third position, Jack has 2 options left, and for the fourth position, there is only 1 option remaining.
To find the total number of ways, we multiply the number of choices for each position together:
4 * 3 * 2 * 1 = 24
So, Jack can hang the 4 flags in 24 different ways.
The correct answer choice is 24.