0
votes
1answer
23 views

AM I doing this right? - How many binary words of length 8 are there that contain at least six 1's?

How many binary words of length 8 are there that contain at least six 1's? This is what I have: 8!/6!2! = 28 words Is this the correct answer?
2
votes
1answer
45 views

Using combinatorial reasoning to show $n!=\binom{n}{0}D_n+\binom{n}{1}D_{n-1}+\dots+\binom{n}{n}D_0$

How can one use combinatorial reasoning to show that $$n!=\dbinom{n}{0}D_n+\dbinom{n}{1}D_{n-1}+\dbinom{n}{2}D_{n-2}+....+\dbinom{n}{n-1}D_1+\dbinom{n}{n}D_0$$ Now $D$ stands for deranged which is a ...
0
votes
1answer
100 views

Exotic 6-horse race betting probabilities

I'm gearing up for horse racing season, and I'm trying to teach some fellow engineering friends how to bet "exotic" bets by using colored dice to simulate horses. So, the odds for each horse winning ...
1
vote
1answer
23 views

Number of orders and combinations

I have just done these two questions and I have answers for them but I am not sure if they are correct. A jazz band is to give one concert in each of nine selected cities. Calculate the total ...
2
votes
0answers
67 views

Find all possible solutions!

Find solutions for $$^nP_r=s!$$ For $(n,r,s)\in \mathbb{N}$ I could find some trivial solutions $(6,3,5)~,~(1,1,1)$ etc.
2
votes
2answers
56 views

Logic of statement

I can see the mathematical implication but could not get the logic, why $5!$ is equal to $^6P_3$? Please help proving why both the expressions are equal without mathematical manipulation!In any case, ...
1
vote
1answer
51 views

How does Knuth's second algorithm to calculate permutations work?

I have started reading the Art of Computer Programming Volume 1 by Knuth. The first half of the book is basic concepts in maths. On page 45 there is an algorithm to obtain the next (amount of) ...
0
votes
3answers
101 views

Why factorials when divided by factorials less than the number have a remainder 0?

Lets take the example, if we take the expression $\frac{X!}{y_1!\cdot y2!\cdots y_n!} $as long as Summation $S=y_1+y_2+...y_n$ is less than or equals $X$, the remainder is always $0$. Thats How the ...
2
votes
1answer
44 views

Solving a permutation/Combination equation

please help check if this would the correct way to solve this: $^nP_2 = ^{n+1}C_3$. I want to solve for $n$. theoretically, I was thinking that: $^nP_k = k!\times ^nC_k $ hence: ...
0
votes
1answer
140 views
2
votes
2answers
154 views

Simple Combinatorics Problem

I've 'indirectly' studied combinatorics earlier in probability courses, but now it's part of the math course I'm taking. I always thought it was very hard, and well, here I am again... The problem ...
1
vote
1answer
259 views

How to calculate the number of permutations and combinations if k is equal to n?

Say the question is How many unique ways are there to arrange the letters in the word FANCY? The formula I use for permutations is n! / (n - k)! ...
0
votes
2answers
193 views

Factorial related problems

How many zeros are there in $ 25!$ ? My answer was $6$. But i solved it by finding how many numbers are divisible by $5$ and $2$.here i was told to find out the zeros at the last end. But what is the ...
3
votes
0answers
40 views

Bound on Permutations [duplicate]

I am trying to prove the following inequality, $$n^{(l)} = n(n-1)\cdots(n-l+1) \geq \frac{n^l}{e}\quad\text{ for }\quad 2 \leq l \leq \sqrt{n}\;.$$ So my approach is to observe that $n^{(l)} = ...
5
votes
2answers
511 views

Ways to add up 10 numbers between 1 and 12 to get 70

I know this has something to do with factorials, and combinations and permutations. I've been puzzling over this for a little while, and I can't come up with an answer. My question is, How would one ...
-4
votes
1answer
124 views

How many factors of $10$ in $100!$ [duplicate]

Possible Duplicate: Highest power of a prime $p$ dividing $N!$ How many factors of 10 are there in $100!$ (IIT Question)? Is it 26,25,24 or any other value Please tell how you have done ...
7
votes
1answer
162 views

Is n! mod p doable in sub O(n) time?

I ask because I can use Lucas Theorem to find n choose k mod p but don't know of an equivalent for permutations (n permute k mod p).
1
vote
0answers
135 views

How to find the last non-zero digit in ${^n\!P_k} $?

What is the procedure of finding the last non-zero element in ${^n\!P_k}$?
-1
votes
1answer
130 views

What do you call a permutation that is no where identity?

I want to write a formula for $n!$. $n!$ is the number of permutation functions on the set $\{1,\ldots,n\}$. Let's define a "true k-permutation" on $\{1,\ldots,n\}$ as a permutation that is identity ...
-4
votes
2answers
801 views

How many ways can we order a set of $n$ elements?

If you have $n$ CDs to arrange sequentially on a shelf, say for $1 \le n \le 20$, how many ways can they be ordered? Please also explain the solution steps.
1
vote
1answer
313 views

Permutation Problem with a Variable

13P5 = 1287(xPx) I simplify the above to: 13!/8! = 1287(x!) The expression on the left simplifies to 154,440. I divide both sides by 1287 to get: 120=x! At this point I'm stumped. Thanks in ...
0
votes
4answers
267 views

Factorial of 0 - a convenience?

If I am correct in stating that a factorial of a number ( of entities ) is the number of ways in which those entities can be arranged, then my question is as simple as asking - how do you conceive the ...
2
votes
3answers
422 views

Arrangement of six triangles in a hexagon

You have six triangles. Two are red, two are blue, and two are green. How many truly different hexagons can you make by combining these triangles? I have two possible approachtes to solving this ...