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Solve the following question
10 friends are planning to travel to Alibag in 2 cars, a Santro and a Swift. If the Swift and the Santro can accommodate 6 and 5 people respectively, in how many ways can the friends travel? (in numerical value)
Correct answer is '462'. Can you explain this answer?
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Solve the following question10 friends are planning to travel to Aliba...
If 6 friends travel in the Swift and 4 travel in the Santro, they can do this in 10C6 = 210 ways.
If 5 friends travel in the Swift and 5 travel in the Santro, they can do this in 10C5 = 252 ways.
Thus the total number of ways is 210 + 252 = 462.
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Solve the following question10 friends are planning to travel to Aliba...
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Solve the following question10 friends are planning to travel to Aliba...
Problem:
10 friends are planning to travel to Alibag in 2 cars, a Santro and a Swift. If the Swift and the Santro can accommodate 6 and 5 people respectively, in how many ways can the friends travel?
Solution:
To find the number of ways the friends can travel, we need to consider the different possibilities of how many friends can travel in each car.
Case 1: All friends travel in the Swift
In this case, all 10 friends will travel in the Swift car. Since the Swift can accommodate 6 people, this is not possible. Therefore, the number of ways for this case is 0.
Case 2: 9 friends travel in the Swift and 1 friend in Santro
In this case, 9 friends will travel in the Swift car and 1 friend will travel in the Santro car. We have 10 friends to choose 1 friend for the Santro car, which can be done in 10 ways. Therefore, the number of ways for this case is 10.
Case 3: 8 friends travel in the Swift and 2 friends in Santro
In this case, 8 friends will travel in the Swift car and 2 friends will travel in the Santro car. We have 10 friends to choose 2 friends for the Santro car, which can be done in 10C2 = 45 ways. Therefore, the number of ways for this case is 45.
Case 4: 7 friends travel in the Swift and 3 friends in Santro
In this case, 7 friends will travel in the Swift car and 3 friends will travel in the Santro car. We have 10 friends to choose 3 friends for the Santro car, which can be done in 10C3 = 120 ways. Therefore, the number of ways for this case is 120.
Case 5: 6 friends travel in the Swift and 4 friends in Santro
In this case, 6 friends will travel in the Swift car and 4 friends will travel in the Santro car. We have 10 friends to choose 4 friends for the Santro car, which can be done in 10C4 = 210 ways. Therefore, the number of ways for this case is 210.
Case 6: 5 friends travel in the Swift and 5 friends in Santro
In this case, 5 friends will travel in the Swift car and 5 friends will travel in the Santro car. We have 10 friends to choose 5 friends for the Santro car, which can be done in 10C5 = 252 ways. Therefore, the number of ways for this case is 252.
Total number of ways:
To find the total number of ways, we need to add up the number of ways for each case.
Total ways = 0 + 10 + 45 + 120 + 210 + 252 = 637
Therefore, the correct answer is 637, not 462 as given in the question.
10 friends are planning to travel to Alibag in 2 cars, a Santro and a Swift. If the Swift and the Santro can accommodate 6 and 5 people respectively, in how many ways can the friends travel?
Solution:
To find the number of ways the friends can travel, we need to consider the different possibilities of how many friends can travel in each car.
Case 1: All friends travel in the Swift
In this case, all 10 friends will travel in the Swift car. Since the Swift can accommodate 6 people, this is not possible. Therefore, the number of ways for this case is 0.
Case 2: 9 friends travel in the Swift and 1 friend in Santro
In this case, 9 friends will travel in the Swift car and 1 friend will travel in the Santro car. We have 10 friends to choose 1 friend for the Santro car, which can be done in 10 ways. Therefore, the number of ways for this case is 10.
Case 3: 8 friends travel in the Swift and 2 friends in Santro
In this case, 8 friends will travel in the Swift car and 2 friends will travel in the Santro car. We have 10 friends to choose 2 friends for the Santro car, which can be done in 10C2 = 45 ways. Therefore, the number of ways for this case is 45.
Case 4: 7 friends travel in the Swift and 3 friends in Santro
In this case, 7 friends will travel in the Swift car and 3 friends will travel in the Santro car. We have 10 friends to choose 3 friends for the Santro car, which can be done in 10C3 = 120 ways. Therefore, the number of ways for this case is 120.
Case 5: 6 friends travel in the Swift and 4 friends in Santro
In this case, 6 friends will travel in the Swift car and 4 friends will travel in the Santro car. We have 10 friends to choose 4 friends for the Santro car, which can be done in 10C4 = 210 ways. Therefore, the number of ways for this case is 210.
Case 6: 5 friends travel in the Swift and 5 friends in Santro
In this case, 5 friends will travel in the Swift car and 5 friends will travel in the Santro car. We have 10 friends to choose 5 friends for the Santro car, which can be done in 10C5 = 252 ways. Therefore, the number of ways for this case is 252.
Total number of ways:
To find the total number of ways, we need to add up the number of ways for each case.
Total ways = 0 + 10 + 45 + 120 + 210 + 252 = 637
Therefore, the correct answer is 637, not 462 as given in the question.
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Solve the following question10 friends are planning to travel to Alibag in 2 cars, a Santro and a Swift. If the Swift and the Santro can accommodate 6 and 5 people respectively, in how many ways can the friends travel? (in numerical value)Correct answer is '462'. Can you explain this answer?
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