John has 9 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?
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There are 362880 different of ways the flags can be arranged in a row

Step-by-step explanation:

Given

Number of flags = 9

Required

Number of arrangements

The question talks about arrangements, this means we're dealing with permutations.

Provided that all flags are distinct, each of the 9 flags can be arranged in 1! way each.

All 9 flags can be arranged in

(1!)^9 = 1 (this number is negligible)

All in all, the total 9 flags can be arranged "collectively" in a row in 9! ways

Calculating 9!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

9! = 362880

Hence, there are 362880 different of ways the flags can be arranged in a row

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!