there are 12 intermediate stations between two places A and B. I n how many ways can a train be made to stop at 4 of these 12 stations that no two stations are consecutive?

1) 15C3
2) 11c3
3) 9c4
4) 9c3

• Since there are 12 stations and 4 stations are stoppage. We remove those 4 stations. Now between A and B there are 8 stations and 9 spaces. (between n stations there are n+1 spaces). Thus there are 9 spaces. Since 4 are stoppage,4 stations can be inserted between 9 gaps in 9C4 ways. Thus answer is 9C4.
• 7 years agoHelpfull: Yes(2) No(1)
• Initially, let’s remove the 4 stopping stations. Then we are left with 8 non-stopping stations (=12-4) as shown below. Explanation to Problem on Permutations and Combinations (non-stopping stations are marked as 1,2 … 8) Now there are 9 positions to place the 4 stopping stations such that no two stopping stations are consecutive. This can be done in 9C4 ways. Hence, required number of ways = 9C4
• 6 years agoHelpfull: Yes(1) No(0)