Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 5 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0,1,2,... , 9 with no repeats. How many serial numbers can be generated

43,200 serial numbers can be generated

Step-by-step explanation:

The ordering for the letters and the digits are important. For example, 012 constitutes a different serial number than 210. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

How many serial numbers can be generated

3 letters, from the first five of the alphabet

3 digits, from a set of 10

So

43,200 serial numbers can be generated

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

addition

step-by-step explanation: