(B) To travel between any two stations,a ticket must be issued for a specific starting station and a specific destination station.Since there are $15$

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(B) To travel between any two stations,a ticket must be issued for a specific starting station and a specific destination station.Since there are $15$ stations,the number of ways to choose a starting station and a destination station is given by the permutation formula $^{n}P_{r}$,where $n = 15$ and $r = 2$.Total number of tickets = $^{15}P_{2} = \frac{15!}{(15-2)!} = 15 \times 14 = 210$.Thus,$210$ different types of tickets are required.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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There are $15$ stations on a railway line. How many different types of tickets must be printed so that a passenger can travel from any station to any other station?

A
$225$
B
$210$
C
$14^{15}$
D
$15^{15}$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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If all the possible $3$-digit numbers are formed using the digits $1, 3, 5, 7, 9$ without repeating any digit,then the number of such $3$-digit numbers which are divisible by $3$ is

EasyTS EAMCET 2024

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The sum of the digits in the unit's place of all the $4-$ digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is:

DifficultJEE MAIN 2014

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If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

MediumAIEEE 2005

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There are $15$ stations on a railway line. How many different types of tickets must be printed so that a passenger can travel from any station to any other station?

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The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

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