Question

FAN+MEDAL+TESTIMONIAL:):)!!

How many arrangements are there of the word MATHEMATICS?
How many of these start with the letter M?
How many of the arrangements in part a have the T’s together?

Answer 1

I think that this is a permutation problem. So given that there are 11 letters in the word math, I will do the following calculation

Answer 2

11P11

Answer 3

Without restrictions

Answer 4

@nincompoop

Answer 5

hai

Answer 6

Hi Sir:)

Answer 7

Am I on the right track?

Answer 8

ya know I'm stuck on this question right now too :P

Answer 9

This is a university level math don't worryXD

Answer 10

:O really? its on my 8th grade quiz

Answer 11

Forgive me I am in a Canadian school.

Answer 12

lol ok i will try to help tho

Answer 13

gimee a sec

Answer 14

Arrangement of letters of a word is a permutation question right?

Answer 15

As opposed to combination

Answer 16

Hi everyone:)

Answer 17

Am I on the right track?

Answer 18

I don't know.

Answer 19

How many arrangements are there of the word MATHEMATICS?
Rule:

Start with the factorial of the number of letters in the word. Then,
for each indistinguishable letter in the word, divide by the factorial
of the number of times that letter occurs in the word.

"MATHEMATICS" is an 11-letter word. If all the letters were
distinguishable like in "MATHEmatICS", the answer would be 11! = 39916800
However, there are
2 indistinguishable M's
2 indistinguishable A's
2 indistinguishable T's

Thus, using the rule, we divide 11! by (2!)(2!)(2!)


\[\frac{ 11! }{ 2!*2!*2! }=\frac{ 39916800 }{ 8 }=4989600\]

How many of these start with the letter M?
That amounts to finding all the distinguishable arrangements
of the 10-letter "word" "ATHEMATICS" and putting an M in the beginning
of each.

"ATHEMATICS" is a 10-letter "word" and it contains

2 indistinguishable A's
2 indistinguishable T's

Thus, using the rule, we divide 10! by (2!)(2!)

\[\frac{ 10! }{ 2!*2! }=\frac{ 3628800 }{ 4 }=907200\]

How many of the arrangements in part a have the T’s together?
That amounts to finding all the distinguishable arrangements
of the 10-letter "word" "MATHEMAICS" and inserting another T to the right
of the "T" in each.

"MATHEMAICS" is a 10-letter "word" and it contains

2 indistinguishable M's
2 indistinguishable A's

Thus, using the rule, it's exactly the same answer as the second part.
We divide 10! by (2!)(2!)

\[\frac{ 10! }{ 2!*2! }=\frac{ 3628800 }{ 4 }=907200\]



There ya go!

Answer 20

YOU ROCK:)

Answer 21

:)

Answer 22

ok testimonial?

Answer 23

let me know if it could be better