How Many 3-Digit Numbers Are Divisible by 5?

  • Thread starter Thread starter zipup
  • Start date Start date
  • Tags Tags
    Permutation
zipup
Messages
3
Reaction score
0
1. 3-digit numbers are constructed from the digits 0,1,2,3,4,5,6,7,8,9 using each digit at most once. How many such number are divisible by 5?



2. Just simply permutation, the answer is 136.



3. 8 x 7 x 2 = 128
 
Physics news on Phys.org


Firstly, 8*7*2 is not equal to 128.

My calculation is:

Firstly for numbers ending in 0,

9*8 possible ways of choosing 2 digits.

For numbers ending in 5,

8*7, since we want to exclude 0

9*8 + 8*7 = 128.
 


Sisplat said:
Firstly, 8*7*2 is not equal to 128.

My calculation is:

Firstly for numbers ending in 0,

9*8 possible ways of choosing 2 digits.

For numbers ending in 5,

8*7, since we want to exclude 0

9*8 + 8*7 = 128.

I think this undercounts by excluding the eight numbers 105, 205, etc. (Eight since 505 is still out.) We just want to exclude 0 from the first digit, not from the second.

The counting then becomes 9*8 + 8*8 = 136, which seems to be desired answer.

PS. Why is this filed under "Advanced Physics" instead of "Precalculus Mathematics"?
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

MHB Solving Permutations Question with Restrictions
Replies
3
Views
1K
MHB How Many Numbers Less Than 1000 Divisible by 5 Are Formed Using Unique Digits?
Replies
1
Views
1K
MHB How many nine-digit numbers meet these criteria?
Replies
1
Views
914
Probability Question: 3-Digit Combination Lock
Replies
3
Views
2K
Combinatorics and set cardinality
Replies
23
Views
2K
Leetcode 728 complier issue with mutliple functions
Replies
12
Views
2K
Proof That an Integer is Divisible by 2
Replies
3
Views
2K
Program to list specific permutations of 5 digits
Replies
4
Views
3K
The units digit of a triangular number iw ## 0, 1, 3, 5, 6 ##?
Replies
1
Views
2K
MHB Solving 6-Digit Number Quandaries: 1, 2, 3, 4, 5, 6
Replies
8
Views
7K

Hot Threads

Recent Insights

Back
Top