Question

Rajdhani Express stops at six intermediate stations between Kota and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is

• A. $\frac{{}^6{P}_5}{6^5}$
• B. $\frac{{}^6{C}_5}{6^5}$
• C. $\frac{{}^7{P}_5}{7^5}$
• D. $\frac{{}^7{C}_5}{7^5}$

Answer 1

The correct option is A $\frac{{}^6{P}_5}{6^5}$

Total number of intermediate Station = 6

Total Number of passenger = 5

Total Number of ways in which the passengers will get down at any station $=6^5$

Number of ways in which all 5 passengers get down at different stations

${=}^6{P}_5$

Hence, Required Probability $=\frac{{}^6{P}_5}{6^5}$