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timurjin [86]
3 years ago
6

for the given license plate configuration, determine how many different plates are possinle if letters and digits (a) can ba rep

eated (b) can not be repeated. 3 letters followed by 2 digits
Mathematics
1 answer:
Inessa05 [86]3 years ago
4 0

Answer:

a) 1,757,600 different plates possible.

b) 1,404,000 different plates possible.

Step-by-step explanation:

The permutations formula is important 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:

P_{(n,x)} = \frac{n!}{(n-x)!}

(a) can be repeated:

There are 3 letters, each one with 26 possible outcomes.

2 digits, each with 10 possible outcomes

So

T = 26*26*26*10*10 = 1757600

1,757,600 different plates possible.

(b) cannot be repeated:

Here the permutations formula is used.

Three letters, from a set of 26.

Two digits, from a set of 10. So

T = P_{(26,3)}*P_{(10,2)} = \frac{26!}{(26-3)!}*\frac{10!}{(10-2)!} = 1404000

1,404,000 different plates possible.

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Well's College in New York was previously an all girls school. In 2005, the college began to allow boys to enroll. By 2012, the
kogti [31]

Answer: 150 boys

Step-by-step explanation:

Let the number of boys be x

Since there were 200 more girls than boys, the number of girls will be: = x + 200

Since the ratio of boys to girls was 3:7, this can be solved further below:

3/7 = x/x+200

Cross multiply

(7 × x) = 3(x + 200)

7x = 3x + 600

7x - 3x = 600

4x = 600

x = 600/4

x = 150

The number of boys enrolled is 150

Number of Girls will be:

= X + 200

= 150 + 200

= 350

Check: Number of boys / Number of girls

= 150/350

= 3/7

= 3:7

7 0
3 years ago
Select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. a
Alexxandr [17]

If the denominator does not equal 0, the equivalent expression of \frac{14x^4y^6}{7x^8y^2} is \frac{2y^{4}}{x^{4}}\frac{x^{10} y^{14}}{729}

<h3>How to determine the equivalent expression?</h3>

The expression is given as:

\frac{14x^4y^6}{7x^8y^2}

Divide 14 by 7

\frac{14x^4y^6}{7x^8y^2} = \frac{2x^4y^6}{x^8y^2}

Apply the law of indices

\frac{14x^4y^6}{7x^8y^2} = \frac{2y^{6-2}}{x^{8-4}}

Evaluate the differences in the exponents

\frac{14x^4y^6}{7x^8y^2} = \frac{2y^{4}}{x^{4}}

Hence, the equivalent expression of \frac{14x^4y^6}{7x^8y^2} is \frac{2y^{4}}{x^{4}}

Read more about equivalent expressions at:

brainly.com/question/2972832

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4 0
2 years ago
How many total inches are in 7 feet 4 inches and 4 feet 10 inches ??? A) 257 inches B) 130 inches C) 126 inches D) 146 inches wh
Gelneren [198K]
The correct answer is D, 146 inches.
7 x 12 = 84
4 x 12 = 48
84+48+4+10 = 146
5 0
3 years ago
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Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random samp
Oxana [17]

Answer:

Step-by-step explanation:

The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.

5 0
2 years ago
Need help???! Explanation too please
Natalija [7]

Answer:

When X=Y every number on either side is the same, for example 1(X)=1(Y)

Step-by-step explanation:

This is because when X=Y the X value isn't altered in any way to equal Y, so they are the same number, hope this helped!

4 0
3 years ago
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