Question:

How many different words can be formed by jumbling the letters in the word in which no two $S$ are adjacent ?

Updated On: Jul 6, 2022

$8\cdot\,^6C_4\cdot\,^7C_4$
$6\cdot 7 \cdot\,^8C_4$
$6\cdot 8\cdot\,^7C_4$
$7\cdot\,^6C_4\cdot\,^8C_4$

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The Correct Option is D

Solution and Explanation

First of all arrange $M, I, I, I, I, P, P$ This can be done in $\frac{7\,!}{4\,!\, 2\,!}$ ways. $\times M \times I\times I\times I\times I\times P\times P\times$ If we place is $S$ at any of the $X$ places then no two $S??$ are together. $\therefore$ total number of ways $=\frac{7\,!}{4\,!\, 2\,!}\cdot^{8}C_{4}$ $=7\times\,^{6}C_{4}\times\,^{8}C_{4}$ ways.

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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence.

In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

Combination refers to the combination of about n things taken k at a time without any repetition.
The combination is used for a group of data where the order of data does not matter.