Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 15-4-2021

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Loading DoubtNut Solution for you

Watch 1000+ concepts & tricky questions explained!

1.0 K+

51

Text Solution

Solution :

The total number of arrangement of the letters of the word ''CONSTANTINOPLE'' is `(14)!//3! 2! 2!` <br> Since 3 N's are consecutive, then considering all the 3 N's as single letter, the total number of arrangements is `(12)!//2! 2!` <br> Therefore, required probability is <br> `=((12)!//(2! 2!))/((14)!//(3! 2! 2!)) = (3!)/(14xx13) = (3)/(91)` Transcript

Time | Transcript |
---|---|

00:00 - 00:59 | the question says that find the probability that the three and come consecutively in the arrangement of the letters of the word konstantinopel should be given to a says c o n s t a and n o p l a so there are a total of 14 letters in it there are 14 letters and some of the letters are repeating like and and so we have three ends to 30 han to pose |

01:00 - 01:59 | superfast we will find total number of ways of selecting arranging these letters total ways of arranging these letters are there are 14 letters and we are 14 spaces so we can arrange them by 14 factorial Although we have three repeating ends to 30 and Tu ose and arranging 3 ends in the place of each other will have no effect on total arrangement similarly 40 and so we have to divide this with 3 factorial for N2 factorial 40 and to factorial for so this is our total ways so now we will go for favourable ways favourable ways the question says that three ends should come |

02:00 - 02:59 | consecutively so we will arrange three consecutive Li and we will treat it like one letter for now so the letters remaining r c s t a t i o p l and so there are 12 letters remaining with considering this as one letter so arranging this 12 letters we have 12th base is so we can write it as 12 factorial but there are some repeating letters also like to anti this 3 are now considered as one group so there |

03:00 - 03:59 | rearranging will know will have no effect on arranging this these two letters so we have to / tutorial for and to factorial 40 sunao probability will become favourable outcomes that is 12 factorial upon to factorial into two factorial divided by total waste that is 14 factorial upon 3 factorial in 22 factorial in 22 factorial now this will become 12 factorial tutorial is 2 into it will be received from local so it is 3 factorial is 3 into 2 into 1 into two factorial is to upon 14 Federal can be written as 14 into 13 into |

04:00 - 04:59 | 12 factorial now these two and these two will cancel these two this 12 October will cancel this 12 factorial na answer will be 3 upon 91 which is the required answer |