What if the authorities of combinatoria degree that (1) the three letters must be distinct, (2) the four digits must also be distinct, and (3) the first of the four digits cannot be 0. now how many distinct license plates are there?

Step-by-step explanation:

Given  that (1) the three letters must be distinct, (2) the four digits must also be distinct, and (3) the first of the four digits cannot be 0.

Out of 26 letters 3 different letters can be arranged if order matters in 26P3 ways

i.e.

4 digits with I digit non zero

So I zero can be selected in 9 ways excluding 0, 3rd digit in 9 ways excluding I digit, 2nd in 8 and 3rd in 7

No of ways

Total no of ways

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.

14

step-by-step explanation:

14 x 3 = 42