Math Algebra 1 Algebra 2 Prealgebra Precalculus Algebra Mathematics

Ally J.

asked 05/03/21a) 30x4! The answer is 720 when you plug it in the calculator, but how can make it to be 6!, 6! = 720, if that makes sense.

b) 7 / 2! 5! + 7! / 4! 3!

I did, 7x6x4x3 = 504, 7x6x5 / 3x2x1 = 84, 84 + 504 = 588 but the answer was supposed to be 56.

c) 9! / 3! 6!

I did 9x8x7x5x4 = 10,080 but the answer was 84.

Follow 1

Comments 2

More

Report

Vidya V.

tutor

Part a) 30*4! = 6*5*4!= 6!Part c) If you do:(9x8x7x6x5x4x3x2x1)/(3x2x1)(6x5x4x3x2x1)=(9x8x7)/(3x2x1)You’ll get the answerI think you might have missed some number Part b) would be 21+ 35= 56I see your mistake now!Ok what you’re doing is you’re just removing the denominator numbers from the numerator- but in the denominator you have 2!*5! Which means your denominator would be (2x1)(5x4x3x2x1)Now you cancel out some numbers in the numbers for and denominator and you would end up having 21 and 35.I hope I have helped you understand.Report

05/03/21

Ally J.

Thank you!!Report

05/03/21

## 2 Answers By Expert Tutors

By:

James C. answered 05/03/21

Tutor

5 (453)

About this tutor›

About this tutor›

The key here is to remember what factorials look like when "expanded" out. In general,

n! = n x (n-1) x (n-2) x , , , x 2 x 1

or

7! = 7x6x5x4x3x2x1

So, for part a, we can make the expression look like 6! by doing the following

30x4! = 30x4x3x2x1

Notice that 30 = 6x5

30x4x3x2x1 = 6x5x4x3x2x1 = 6!

For part b, if we expand out each factorial, we will see a lot of cancelling between the numerator and denominator. I will give an example of the second half of part b and then let you take it from there.

7! / 4! 3! = 7x6x5x4x3x2x1 / (4x3x2x1)x(3x2x1)

Notice that 3x2x1 = 6

7x6x5x4x3x2x1 / (4x3x2x1)x6

Now notice that there is a 4,3,2,1, and 6 on top and bottom of the fraction, so we can cancel those out,

7x5 = 35

(remember that this is only the second half of part b, you can confirm that the first half is equal to 21, meaning the answer is 56 as you said)

Upvote 1 Downvote

Comments 4

More

Report

Ally J.

Thank you so much, but what if it was a bigger number like 90x8! Or 20x19! ? Second part, But the thing that I’m confused about is that it is very similar to question that I did before which is 9! / 3! 6!, 9x8x7x6x5x4x3 (up to 3!) cancel the 3! numerator and denominator and the 6! as well, and my answer was 10,080 which was correct. Did the exact same thing, that’s why I was confused.Report

05/03/21

James C.

tutor

For the first part, this process will work regardless of the size of the number. They key is to factor the larger number into numbers that can be "absorbed" into the factorial, for the example you gave, 90x8! = 10x9x8! = 10!As for the second part, it is hard to give a definite answer without seeing the problem you are talking about. It is also possible to just get lucky and make 2 mistakes that cancel each other out when calculating a factorial like these. This method will definitely get you the correct result every time, though.Report

05/03/21

Ally J.

For 20x19! I did (5x4=20) 5x4x3x2x1 = 5! Which was incorrect. I realised my mistake for part b) your way was better!Report

05/03/21

Ally J.

Also what if it was 21! / 17!4!, I did 21x20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1 / (17x16x15x14x13x12x11x10x9x8x7x6x5x3x2x1)x(4x3x2x1)=24, so cancel 17s,16s,15s,14s.....1s I was left with 21x20x17x18 / 4x3x2x1, and still got the answer wrong.Report

05/03/21

Raymond B. answered 05/03/21

Tutor

5 (2)

Math, microeconomics or criminal justice

See tutors like this

See tutors like this

a) 30 x 4! = 6 x 5 x 4! = 6! (30=6x5)

6! = 30 x 4! = 720

either = 6(5)(4)(3)(2)(1) = 30x24= 720

b) 7!/2!5! + 7!/3!4! = 7(6)/2 + 7(6)(5)/3(2) = 21 +35 =56

You seem to have omitted ! after the first 7

c) 9!/3!6! = 9(8)(7)/3(2) = 3(4)7) = 84

9!= 9(8)(7)(6!) the 6! cancels with the 6! in the denominator leaving

9(8)(7)/3(2)(1). 3 divides into 9 = 3 and 2 divides into 8 = 4 leaving

3(4)(7) = 12(7) = 84

Upvote 1 Downvote

Add comment

More

Report

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

### RELATED TOPICS

Calculus Geometry Trigonometry Statistics Probability Elementary Math Word Problem Equations Maths Functions ... Word Problems Algebra Help College Algebra Math Help Math Question Math Equations Algebra Word Problem Math Word Problem Math Problem Math Help For College

### RELATED QUESTIONS

what are all the common multiples of 12 and 15Answers · 9

need to know how to do this problemAnswers · 8

what are methods used to measure ingredients and their units of measureAnswers · 8

how do you multiply moneyAnswers · 6

spimlify 4x-(2-3x)-5Answers · 14