12. If the letters of the word "ALGORITHM" are arranged at random in a

1.	12. If the letters of the word "ALGORITHM" are arranged at random in a row, what is theprobability that the letters G, O and R must remain together?
Answer» Required probability =Number of favorable outcomesTotal number of outcomesNumber of favorable outcomesTotal number of outcomes Step 1: Given word ALGORITHM Number of letters in the word =9 The word is arranged randomly. ∴∴Total number of outcomes n(S)=9! Given GOR have to remain together Thereby considering GOR as a single letter ∴∴No of letter=7 Number of favorable outcomes n(E) =7! Step 2: ∴∴Required probability =n(E)/n(S) ⇒7!/9!⇒ 1/9×8 ⇒172

12. If the letters of the word "ALGORITHM" are arranged at random in a row, what is theprobability that the letters G, O and R must remain together?

Answer»

Required probability =Number of favorable outcomesTotal number of outcomesNumber of favorable outcomesTotal number of outcomes

Step 1:

Given word ALGORITHM

Number of letters in the word =9

The word is arranged randomly.

∴∴Total number of outcomes n(S)=9!

Given GOR have to remain together

Thereby considering GOR as a single letter

∴∴No of letter=7

Number of favorable outcomes n(E) =7!

Step 2:

∴∴Required probability =n(E)/n(S)

⇒7!/9!⇒

1/9×8

⇒172