Question

Consider the word $W=MISSISSIPPI$ Number of ways in which the letters of the word W can be arranged if at least one vowel is separated from rest of the vowels

• A. $\frac{8!.16!}{4!.4!.2!}$
• B. $\frac{8!.16!}{4.4!.2!}$
• C. $\frac{8!.16!}{4!.2!}$
• D. $\frac{8!}{4!.2!}.\frac{165}{4!}$

Answer 1

The correct option is A $\frac{8!.16!}{4!.4!.2!}$

W = MISSISSIPPI , Letters= 11

1 M. 4I's, 4S's, 2P's

Total number of arranging these letters

$=\frac{11!}{4!4!2!}$

Suppose all I's are together , then the Number of ways

$=\frac{(1+1+4+2)!}{4!2!}=\frac{8!}{4!2!}$

$\therefore$ Number of ways in which atleast one vowel is separated

$=\frac{11!}{4!4!2!}-\frac{8!}{4!2!}=\frac{8!16!}{4!4!2!}$