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In how many different ways can a train navel from F to A without passing through any station more than once?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In how many different ways can a train navel from F to A without passi...
For travelling F to A, possible routes are:
(i) F D E A
(ii) F D E C A
(iii) F D E G C A
(iv) F D H G C A
Number of possible routes are 4, so option (d) is correct
(i) F D E A
(ii) F D E C A
(iii) F D E G C A
(iv) F D H G C A
Number of possible routes are 4, so option (d) is correct
Most Upvoted Answer
In how many different ways can a train navel from F to A without passi...
Number of Ways to Travel from F to A
To find the number of different ways a train can travel from station F to station A without passing through any station more than once, we can use the concept of permutations.
Permutations: Permutations refer to the arrangement of objects in a specific order. In this case, the objects are the stations between F and A, and we need to find the number of arrangements without repetition.
Approach:
1. We know that there are 4 stations between F and A (excluding F and A).
2. To travel from F to A without passing through any station more than once, the train can take the following routes:
a) F -> B -> C -> D -> A
b) F -> B -> D -> C -> A
c) F -> C -> B -> D -> A
d) F -> C -> D -> B -> A
Explanation:
- In the first route (F -> B -> C -> D -> A), the train starts at F, moves to B, then to C, then to D, and finally reaches A.
- Similarly, the second route (F -> B -> D -> C -> A) starts at F, moves to B, then to D, then to C, and finally reaches A.
- The third route (F -> C -> B -> D -> A) starts at F, moves to C, then to B, then to D, and finally reaches A.
- The fourth route (F -> C -> D -> B -> A) starts at F, moves to C, then to D, then to B, and finally reaches A.
Each of these routes is unique and satisfies the condition of not passing through any station more than once. Therefore, there are 4 different ways for the train to travel from F to A.
Hence, the correct answer is option 'D' (4).
To find the number of different ways a train can travel from station F to station A without passing through any station more than once, we can use the concept of permutations.
Permutations: Permutations refer to the arrangement of objects in a specific order. In this case, the objects are the stations between F and A, and we need to find the number of arrangements without repetition.
Approach:
1. We know that there are 4 stations between F and A (excluding F and A).
2. To travel from F to A without passing through any station more than once, the train can take the following routes:
a) F -> B -> C -> D -> A
b) F -> B -> D -> C -> A
c) F -> C -> B -> D -> A
d) F -> C -> D -> B -> A
Explanation:
- In the first route (F -> B -> C -> D -> A), the train starts at F, moves to B, then to C, then to D, and finally reaches A.
- Similarly, the second route (F -> B -> D -> C -> A) starts at F, moves to B, then to D, then to C, and finally reaches A.
- The third route (F -> C -> B -> D -> A) starts at F, moves to C, then to B, then to D, and finally reaches A.
- The fourth route (F -> C -> D -> B -> A) starts at F, moves to C, then to D, then to B, and finally reaches A.
Each of these routes is unique and satisfies the condition of not passing through any station more than once. Therefore, there are 4 different ways for the train to travel from F to A.
Hence, the correct answer is option 'D' (4).
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Community Answer
In how many different ways can a train navel from F to A without passi...
For travelling F to A, possible routes are:
(i) F D E A
(ii) F D E C A
(iii) F D E G C A
(iv) F D H G C A
Number of possible routes are 4, so option (d) is correct
(i) F D E A
(ii) F D E C A
(iii) F D E G C A
(iv) F D H G C A
Number of possible routes are 4, so option (d) is correct
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