There are 12 intermediate stations between two places A and B. Find the number…
2023
There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?
- A.
9C6
- B.
9C7
- C.
9C4
- D.
9C9
Attempted by 55 students.
Show answer & explanation
Correct answer: C
Answer: 9C4 = 126
Method: Let the chosen stopping stations be s1 < s2 < s3 < s4. To ensure no two are consecutive, define t1 = s1, t2 = s2 - 1, t3 = s3 - 2, t4 = s4 - 3. These transformed positions satisfy 1 ≤ t1 < t2 < t3 < t4 ≤ 9, so they correspond to choosing any 4 distinct positions from the numbers 1 through 9. Therefore the number of valid choices is C(9,4).
Numeric value: C(9,4) = 126.