The serial number on a bill consists of a letter followed by seven digits and then a letter. How many different serial numbers are possible, given the following conditions? (a) Letters and digits cannot be repeated. (b) Letters and digits can be repeated. (c) The letters are nonrepeated consonants and the digits can be repeated. (Let y be a consonant.)

Answers

Answer 1

Answer:

(a) Letters and digits that cannot be repeated will be 39,31,20,000.

(b) Letters and digits that can be repeated will be 6.76 × 10⁹.

What are permutation and combination?

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

The serial number on a bill consists of a letter followed by seven digits and then a letter.

A) Letters and digits cannot be repeated. Then the number of ways will be

⇒ 26 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 25

⇒ 39,31,20,000

B) Letters and digits can be repeated. Then the number of ways will be

⇒ 26 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 26

⇒ 6.76 × 10⁹

C) The letters are non-repeated consonants and the digits can be repeated.

⇒ (5 x 10⁷ x 5) + (21 x 10⁷ x 5) + (5 x 10⁷ x 21)

⇒ 0.25 × 10⁹ + 1.05 × 10⁹ + 1.05 × 10⁹

⇒ 2.35 × 10⁹

More about the permutation and the combination link is given below.

brainly.com/question/11732255

#SPJ2

Answer 2

Answer:

Answer:

408,844,800.

Step-by-step explanation:

(a) There are 26 letters in the alphabet and 10P7 ways of ordering 7 digits.

10P7 = 10!/3! = 604800

The answer is 26* 604800 * 26

= 26^2 * 604800

= 408844800.

Related Questions

I need help please ASAP!!!
What is the formula for the Pythagorean theory?
Which is the expanded form of 3.69?
how many liters of a 20% alcohol solution should be mixed with a 50 liters of a 60% alcohol solution to obtain a 30% solution?
For a field trip,4 chaperones are needed for every 18 students. How many chaperones are needed if there are 81 students going on the trip

An object is sold for $2 but is on sale for 40% off. What is the final price?

Answers

5 cents or $1.20 I'm not fully sure but it's one of the two

Simplify.

n 6 · n 5 ÷ n 4 · n 3 ÷ n 2 · n

Answers

Answer: $n^(9)$

Step-by-step explanation:

Given expression: $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$

The law of exponents are given by :_

$a^m\cdot a^n=a^(m+n)\n\na^m/ a^n=a^(m-n)$

Using PEDMAS, first we solve division, we get

$n^6\cdot n^(5-4)\cdot n^(3-2)\cdot n\n\n=n^6\cdot n\cdot n\cdot n$

Now, using product law of exponent we get

$n^(6+1+1+1)\n\n=n^(9)$

Answer:

The given expression $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$ is $n^9$

Step-by-step explanation:

Given : Expression $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$

We have to write the simplified form for the given expression $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$

Consider the given expression $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$

Rewrite it in simpler form, we have,

$n^6\cdot(n^5)/(n^4)\cdot (n^3)/(n^2)\cdot n$

Apply exponent rule, $\:a^b\cdot \:a^c=a^(b+c)$ , we have,

$n^6n=\:n^(6+1)$

$=(n^5)/(n^4)\cdot (n^3)/(n^2)n^(7)$

Apply exponent rule, $(x^a)/(x^b)=x^(a-b)$

$(n^5)/(n^4)=n^(5-4)$

$(n^3)/(n^2)=n^(3-2)$

Expression becomes,

$=n^7nn$

Again apply exponent rule, we have,

$\:a^b\cdot \:a^c=a^(b+c)$

$=n^(1+1+7)=n^9$

Thus, The given expression $n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n$ is $n^9$

HELP ME PLS PLS PLSZLZLDBFKSBJZBABS

Answers

Answer:

Step-by-step explanation:

0< $(769000)/(23)$

Simplify the expression (3+5)6

Answers

Answer:

Step-by-step explanation:

(3+5)6

(8)6

Answer:

Step-by-step explanation:

since three+five is in parentheses you do that first which equals eight then eight times six equals forty-eight and that is your Answer

a square wrestling mat has a perimeter of (12x - 32) feet. Write an expression in simplest form that represents the side length of mat.

Answers

In a square, all four sides are equal, so you would take the perimeter and divide by 4.

(12x - 32)/4 = 3x - 8 feet

How do I distribute 9 - (8r +5)
The - part confuses me

Answers

Answer:

you distribute the - not the 9

Step-by-step explanation:

so your problem would be

9-8r-5

( act as if there is a one in front of the negative sign)

hope this helps :)

Other Questions

A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.A. 9p + 11.5p = $94.75; p = $4.62 B. 9(p + $11.50) = $94.75; p = $5.00 C. 9p + $11.50 = $94.75; p = $11.75 D. 9p + $11.50 = $94.75; p = $9.25

What are the trigonometric ratios

Luis has about 700 baseball cards. What is the greatest amount of cards Luis could have that would round to 700

Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What is the total amount of material she needs? A. 3 1/2 yards B. 3 2/3 yards C. 4 yards D. 4 3/8 yards Mark for review (Will be highlighted on the review page)