TS EAMCET · Maths · Permutation Combination
There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at atleast two consecutive stations, then the number of ways in which the train can be stopped is
- A \({ }^{11} \mathrm{C}_5\)
- B \({ }^{15} \mathrm{C}_5\)
- C \({ }^{15} \mathrm{C}_5-{ }^{11} \mathrm{C}_5\)
- D \({ }^{15} \mathrm{C}_{10}-{ }^9 \mathrm{C}_5\)
Answer & Solution
Correct Answer
(C) \({ }^{15} \mathrm{C}_5-{ }^{11} \mathrm{C}_5\)
Step-by-step Solution
Detailed explanation
\( \text{Total ways to stop at 5 stations} = {}^{15}\mathrm{C}_5 \) \( \text{Ways to stop at 5 stations with no two consecutive} = {}^{15-5+1}\mathrm{C}_5 = {}^{11}\mathrm{C}_5 \)…
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