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Solution
The correct option is C 33810
In the given word MISSISSIPPI, I appears 4 times ,
S appears 4 times, P appears 2 times, and M appears just once.
Therefore, number of distinct permutations of the letters in the given word =11!4×4×2=34650
There are 4I's in the given word. When they occur together, they will be treated as a single object for the time being. This single object together with the remaining 7 objects will account for 8 objects.
In these 8 objects, there are 4 Ss and 2 Ps which can be arranged in =8!4×2=840
Thus, number of distinct permutations of the letters of MISSISSIPPI in which 4 I's do not come together = 34650 - 840 = 33810
Given the word "MISSISSIPPI", consider each of the letters of the given word once. Each letter can differ from each other because of uppercase/lowercase and color [ for example green A is different from blue A ]. You can choose 8 different colors. What is the probability that if you arrange these letters randomly, you get the word "MISSISSIPPI" again? [ it doesn't have to be uppercase and there's no restriction on colors, as long as the word is the same ]. The result should be $\frac{1}{34650}$. This is how I tried to solve it, but I couldn't get the exact result.
MISSISSIPPI is composed of 4 distinct letters: M-I-S-P.
Since each letter can differ because of color and uppercase/lower case we have these amount of choices for the letters:
4 distinct letters * 2 character types [ uppercase/lowercase] * 8 different colors = 64 different letters
The probability of arranging the words and getting MISSISSIPPI again is: $P[A] = \frac{number\space of\space arrangements\space that\space contain\space the\space word\space mississippi}{total \space arrangements}$
I calculated the number of total arrangements like this:
We have a total of 64 different letters taken 11 at a time, because the word MISSISSIPPI is composed of 11 letters. Since repetitions are allowed and order matters, we have $64^{11}$ total arrangements of these 64 letters because we have to do 11 choices and we have 64 options for each choice.
Now let's calculate in how many arrangements we get the word "mississippi".
We still have to make 11 choices with repetitions and order.
First letter has to be an M, it can be uppercase/lowercase and can be of 8 different colors, so we have
1 letter * 2 character types [uppercase/lowercase] * 8 colors = 16 different way of getting an M
Same reasoning can be done with every letter of the word "missisippi", so we have 16 options for each choice every time and we have a total of 11 choices, so the number of arrangements with the word "missisippi" are $16^{11}$.
Let's calculate $P[A]$
$P[A] = \frac{16^{11}}{64^{11}} = \frac{2^{44}}{2^{66}} = \frac{1}{2^{22}} = \frac{1}{4194304} $
What did I do wrong?
15. How many eleven- letter patterns can be formed from the letters of the word Mississippi ? A. C. 11-1 B. frac 1114!4!2! D. frac 11!4!32!
Question
Gauthmathier6678
Grade 11 · 2021-06-09
YES! We solved the question!
Check the full answer on App Gauthmath
15. How many eleven- letter patterns can be formed from the letters of the word Mississippi ?
A.
C.
15. How many eleven- letter patterns can be formed - Gauthmath
B.
\frac {111}{4!4!2!}
D.
\frac {11!}{4!32!}
Liam
Answer
Explanation
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