Answer:
1680 is the answer.
Step-by-step explanation:
Here, we have 11 letters in the word MISSISSIPPI.
Repetition of letters:
M - 1 time
I - 4 times
S - 4 times
P - 2 times
As per question statement, we need a substring MISS in the resultant strings.
So, we need to treat MISS as one unit so that MISS always comes together in all the strings.
The resultant strings will look like:
xxxxMISSxxx
xxMISSxxxxx
and so on.
After we treat MISS as one unit, total letters = 8
Repetition of letters:
MISS - 1 time
I - 3 times
S - 2 times
P - 2 times
The formula for combination of letters with total of n letters:
[tex]\dfrac{n!}{p!q!r!}[/tex]
where p, q and r are the number of times other letters are getting repeated.
p = 3
q = 2
r = 2
So, required number of strings that contain MISS as substring:
[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]
So, 1680 is the answer.
