There are 5 letters in the word "prime"
Imagine we had 5 slots to fill. They are empty initially.
Slot 1 has 5 choices to pick from
Once we pick a letter, we have 4 choices left over for slot 2
Slot 3 will have 3 choices
Slot 4 will have 2 choices
Slot 5 will have 1 choice
We have this countdown: 5,4,3,2,1
which multiplies out to 5*4*3*2*1 = 120
There are 120 unique ways to arrange the letters. Order matters. Because order matters, this is a permutation.
Answer:

Step-by-step explanation:


ANSWER

EXPLANATION
The general term for the sequence is

To find the 55th term, we have to substitute

in to the general term and simplify.
This implies that,




Therefore the 55th term is 161.
Answer:
The common ratio r = 2.
Step-by-step explanation:
Now s2 = a1r and s4 = a1r^3 where a1 = first term and r = common ratio so
s4 / s2 = a1r^3 / a1r = r^2 = 32/8
r^2 = 4
r = 2.