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If a train, five seats are vacant, the n...

If a train, five seats are vacant, the number of ways three passengers can sit, is

A

10

B

20

C

30

D

60

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of how many ways three passengers can sit in five vacant seats on a train, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Number of Seats and Passengers**: - We have 5 vacant seats and 3 passengers. 2. **Choose Seats for the Passengers**: - The first passenger can choose any of the 5 seats. - After the first passenger has chosen a seat, there are 4 seats left for the second passenger. - After the second passenger has chosen a seat, there are 3 seats left for the third passenger. 3. **Calculate the Total Arrangements**: - The total number of ways the passengers can sit is calculated by multiplying the number of choices for each passenger: \[ \text{Total Ways} = 5 \times 4 \times 3 \] 4. **Perform the Calculation**: - Calculate \(5 \times 4 = 20\) - Then multiply that result by 3: \[ 20 \times 3 = 60 \] 5. **Conclusion**: - Therefore, the total number of ways three passengers can sit in five vacant seats is **60**. ### Final Answer: The number of ways three passengers can sit in five vacant seats is **60**. ---
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