How many different arrangements can be made with the letters from the word topic?

 The total number of different arrangements is 120.

Step-by-step explanation:  We are given to find the total number of different arrangements that can be made with the letters from the word "topic".

The total number of letters in the word "topic"  =  5.

We know that

if there are n things, then the total number of different arrangements that can be made using "n" things is n!.

So, the total  total number of different arrangements that can be made using 5 letters will be

5! = 5 × 4 × 3 × 2 × 1 = 120.

Thus, there will be 120 different arrangements.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.