1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
frozen [14]
2 years ago
8

0/1 For positive integer n, n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?. What is the value of 4# · 3# · 2# · 1#?

Mathematics
1 answer:
MakcuM [25]2 years ago
7 0

Answer:

331776

Step-by-step explanation:

Since n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?

Then 4# = 4? · (4 − 1)? · (4 − 2)?· 1?

= 4? · 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 4? = 4! · (4 − 1)! · (4 − 2)! · 1! = 4! · 3! · 2! · 1! = 288

Thus, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Also, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 4# = 4? · 3? · 2?· 1? = 288 × 12 × 2 × 1 = 6912

We now find 3#

3# = 3? · (3 − 1)? · 1? = 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Thus, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 3# = 3? · 2?· 1? = 12 × 2 × 1 = 24

We now find 2#

2# = 2? · (2 − 1)? · 1? = 2? · 1?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 2# = 2?· 1? = 2 × 1 = 2

We now find 1#

1# = 1? · 1? = 1? · 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

And, 1# = 1? · 1? = 1 × 1 = 1

So,  4# · 3# · 2# · 1#? =  6912 · 24 · 2 · 1? = 331776

You might be interested in
Donnie's dad is 3 times older than Donnie, and the sum of their ages is no less than 56. What is the youngest that Donnie can be
Gala2k [10]

Answer:

14

Step-by-step explanation:

If Donnie is 3 times younger than Donnie's dad, that adds up to four parts. In other words, Donnie is 1/4 his dads age. So, divide 56 by four and you have Donnie's age. The rest is Donnie's dad age.

4 0
3 years ago
A rectangular patio has a length of 12 1\2 feet and an area of 103 1\8 square feet. What is the width of the patio?
Whitepunk [10]

Answer:

8.25 feet

Step-by-step explanation:

to find the width, you divide the area by the length

103 1/8 / 12 1/2 = 8.25

Give brainliest, please!
Hope this helps :)

8 0
1 year ago
How to write 710,200 in word form
photoshop1234 [79]
Seven hundred ten thousand and two hundred
7 0
2 years ago
Read 2 more answers
8. How does a tree diagram give you the
Musya8 [376]

Answer:

Read below.

Step-by-step explanation:

The total number of branches end of the tree is the denominator of the fraction form of probability.

All the total possible outcomes in an organized list will give you a denominator because that's all the outcomes that can happen from that set of data.

5 0
3 years ago
In point slope form: passes through (1, -3), slope = -1?​
sleet_krkn [62]

Answer:

y + 3 = -1(x-1)

Step-by-step explanation:

sub (1, -3) and slope = -1:

y - (-3) = -1(x - 1)

Topic: Coordinate Geometry

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

5 0
3 years ago
Other questions:
  • Matrix is handing out treats at a local protest to promote his new detective agency. He allows each participant to reach into hi
    9·2 answers
  • What is the x value of 10=-x-8-6
    11·1 answer
  • A boat travels x miles per hour upstream on the Mississippi River. On the return trip, the boat travels 2 miles per hour faster.
    10·1 answer
  • In which number is the value of the 7 ten times the value of 7 in the number 1,273?
    13·2 answers
  • Two rentalCar companies charge different prices when you rent a car. Company a charges $.28 per mile and a $50 fee. Company B ch
    6·1 answer
  • 50 decreased by twice a number
    5·2 answers
  • from a group of 6 candidates, a committee of 2 people is selected. in how many different ways can the committee be selected?
    7·1 answer
  • Determine the slope of a line that contains the points (6,7) and (5,1)​
    5·2 answers
  • <~~• ¥ Pls HELP me!! ¥ • ~~>
    12·1 answer
  • 42. Rosa incorrectly calculates the product of 4.162 and 2.5 as shown.Line 1:4.162Line 2: X 2.5Line 3: 20810Line 4: 83240Line 5:
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!