Question

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

contain the substring of MISS?

Answer 1

1680 is the answer.

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:

`(n!)/(p!q!r!)`

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:

`(8!)/(3!2!2!)\\\Rightarrow (40320)/(6* 2 * 2)\\\Rightarrow 1680`

So, 1680 is the answer.