Suppose in a state, license plates have two letters followed by four numbers, in a way that no letter or number is repeated in a single plate. Determine the number of possible license plates for this state

3,276,000 possible license plates for this state

Step-by-step explanation:

The order is important. For example, if the letters are EM, it is already a different plate than if the letters were ME. 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:

Letters

There are 26 letters in the alphabet. In the plate, there are two letters. So permutations of two from a set of 26.

Digits

There are 10 digits. In the plate, there are four. So permutations of 4 from a set of 10

Total

Multiplying these values

650*5040 = 3,276,000

3,276,000 possible license plates for this state

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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