How many different license plates are possible if each contains 2 letters(out of the alphabet’s 26 letters) followed by 5 digits (from 0 to 9)? how many of these license plates contain no repeated letters and no repeated digits?

total number of license plates : 676000

total number of license plates with no repeated letters and no repeated digits : 468000

Step-by-step explanation:

i) the license plate is to be made up of two letters (out of 26 alphabets) followed by 5 digits ( from 0 to 9).

therefore the total number of combinations for license plates when repetitions of digits and numbers are allowed will be given

26 × 26 × 10 × 10 × 10 = 676000

ii) the number of license plates containing no repeated letters and no repeated digits will be given by

26 × 25 × 10 × 9 × 8 = 468000

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

9

step-by-step explanation: