Permutation Problems

Agnishom · 2014-08-30 01:26:31

In how many ways can you arrange the characters of MATHEMATICS with the vowels in that order?

bobbym · 2014-08-30 01:31:49

Hi;

EM:

s1 = Permutations[{m, a, t, h, e, m, a, t, i, c, s}, {11}];
Cases[s1, {___, a, ___, e, ___, a, ___, i, ___}] // Length

Analytically:

gAr · 2014-09-06 15:15:06

Hi,

Using bobbym's idea to do it with Sage and unix-like systems utilities:

import os
plst = Permutations("mathematics").list() 
fo = open("tmpf", "w")
for pp in plst:
     fo.write(''.join(pp)+"\n")
fo.close()
os.system("cat tmpf | grep ".*a.*e.*a.*i" | wc -l")

danaj · 2014-09-06 21:05:21

Since I just added a permutation iterator to my module yesterday, this is a convenient time to try it. Using the hash to not count duplicates.

my %h;
my @m = split "", "mathematics";
forperm {
  my $s = join "", @m[@_];
  undef $h{$s} if $s =~ /a.*e.*a.*i/;
  # alternate:  undef $h{$s} if $s =~ tr/aeiou//cdr eq "aeai"
} scalar(@m);
say scalar keys %h;

Result match's Bobbym's analytic answer. Thanks for the fun!

Agnishom · 2014-09-14 20:08:51

2. In how many ways can you pick 4 objects from 5 kabooblydos, 4 carrots, 3 transparent soaps and arrange them on four different plates such that each contains exactly one object?

bobbym · 2014-09-15 00:26:25

Hi;

I am not following the plate idea. How does that make it different from any arrangement problem?

Agnishom · 2014-09-15 00:34:11

It is the same thing, you just pick four objects and arrange them. E.g, KCTT and TTCK are distinct.

bobbym · 2014-09-15 00:39:29

Repetitions are allowed, you are sure?

anonimnystefy · 2014-09-15 00:40:43

I am getting 80, but might be incorrect. Had to do it by hand.

Agnishom · 2014-09-15 00:48:24

bobbym wrote:

Repetitions are allowed, you are sure?

example?

bobbym · 2014-09-15 00:49:36

80 is correct.

anonimnystefy · 2014-09-15 00:50:03

I think repetitions must be allowed. If not, the solution is 0.

bobbym · 2014-09-15 00:51:57

A sim is needed.

Agnishom · 2014-09-15 01:03:22

It cannot be called a sim but I will write it.

Unfortunately, the person who will review the solution knows nothing about EM

bobbym · 2014-09-15 01:04:45

Examine and multiply by the correct constant the coefficient of x^4.

Permutations[{k, k, k, k, k, c, c, c, c, t, t, t}, {4}]//Length

Agnishom · 2014-09-15 01:07:12

Why is each term of the gf divided by some factorial?

bobbym · 2014-09-15 01:08:38

Because this is an exponential gf not an ordinary one. Exponential ones count when order counts.

anonimnystefy · 2014-09-15 01:11:48

I also did it with that GF.

Agnishom · 2014-09-15 01:12:37

Unfortunately the person reviewing the solution is 16 and has no idea what a GF is, nor do I know enough to explain him about it.

anonimnystefy · 2014-09-15 01:14:24

16 is old enough.

You can do it by casework, then.

bobbym · 2014-09-15 01:15:00

I know you did.

Unfortunately, the person who will review the solution knows nothing about EM

There are many ways to solve a problem. Good mathematicians do not criticize how you do it generally. See the big boys on the SE.

Agnishom · 2014-09-15 01:18:19

I will have to ask Rakesh to solve it for him.

Can I see the casework solution please?

bobbym · 2014-09-15 01:19:58

It will take time to write up it is lengthy and ugly.

anonimnystefy · 2014-09-15 01:20:45

Hm, you just list out all the possibilities.

bobbym · 2014-09-15 01:22:17

That is why casework is junk and I prefer generating functions. It will take me about an hour to latex it up and therefore it will take several hours.

Math Is Fun Forum

#1 2014-08-30 01:26:31

Permutation Problems

#2 2014-08-30 01:31:49

Re: Permutation Problems

#3 2014-09-06 15:15:06

Re: Permutation Problems

#4 2014-09-06 21:05:21

Re: Permutation Problems

#5 2014-09-14 20:08:51

Re: Permutation Problems

#6 2014-09-15 00:26:25

Re: Permutation Problems

#7 2014-09-15 00:34:11

Re: Permutation Problems

#8 2014-09-15 00:39:29

Re: Permutation Problems

#9 2014-09-15 00:40:43

Re: Permutation Problems

#10 2014-09-15 00:48:24

Re: Permutation Problems

#11 2014-09-15 00:49:36

Re: Permutation Problems

#12 2014-09-15 00:50:03

Re: Permutation Problems

#13 2014-09-15 00:51:57

Re: Permutation Problems

#14 2014-09-15 01:03:22

Re: Permutation Problems

#15 2014-09-15 01:04:45

Re: Permutation Problems

#16 2014-09-15 01:07:12

Re: Permutation Problems

#17 2014-09-15 01:08:38

Re: Permutation Problems

#18 2014-09-15 01:11:48

Re: Permutation Problems

#19 2014-09-15 01:12:37

Re: Permutation Problems

#20 2014-09-15 01:14:24

Re: Permutation Problems

#21 2014-09-15 01:15:00

Re: Permutation Problems

#22 2014-09-15 01:18:19

Re: Permutation Problems

#23 2014-09-15 01:19:58

Re: Permutation Problems

#24 2014-09-15 01:20:45

Re: Permutation Problems

#25 2014-09-15 01:22:17

Re: Permutation Problems

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