Question

The numbr of arrangement that can be made out the letters of the world 'MISSISSIPI' so that all the S''s come together and I's not come together is

• A. 188
• B. 186
• C. 185
• D. 190

Answer 1

Answer: (B)

186

According to Question,

we have.........MISSISSIPI,

M(1), S(4), I(4), P(1)

Total No. of arrangement,when all S comes together ,

=$\frac{7!}{4!}$

and, total No.of arrangement, when all S's comes together and all I's comes together,

= 4!

Required No. of ways=

$$\begin{array}{c}=\frac{7!}{4!}-4!\\ =\frac{7\times 6\times 5\times 4!}{4!}-4!\\ =7\times 6\times 5-4\times 3\times 2\\ =210-24=186\end{array}$$

So,the correct option is B.