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adell [148]
3 years ago
14

How many strings can be formed by ordering the letters MISSISSIPPI which

Mathematics
1 answer:
Mazyrski [523]3 years ago
3 0

Answer:

<em>1680 is the answer.</em>

Step-by-step explanation:

Here, we have 11 letters in the word <em>MISSISSIPPI.</em>

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 <em>MISS always comes together in all the strings</em>.

The resultant strings will look like:

<em>xxxxMISSxxx</em>

<em>xxMISSxxxxx</em>

<em>and so on.</em>

After we treat <em>MISS </em>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 <em>n </em>letters:

\dfrac{n!}{p!q!r!}

where <em>p, q</em> and <em>r</em> are the number of times other letters are getting repeated.

<em>p = 3</em>

<em>q = 2</em>

<em>r = 2</em>

<em></em>

So, required number of strings that contain MISS as substring:

\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680

So, <em>1680 is the answer.</em>

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