In how many ways can a lift holding eight passenger carry a part of thirteen in two journey?
13C8+13C7 = 3003
can choose to take 8, 7,6 or 5 passangers on the first journey. then the remaining passangers could confirtably be catered for when he comes back.
so (13C8+13C7+13C6+13C5)
To calculate the number of ways a lift can carry a group of 13 people in two journeys, we can use the concept of combinations.
First, let's consider the possible scenarios:
1. In the first journey, the lift can carry 0, 1, 2, 3, 4, 5, 6, 7, or 8 passengers.
2. The number of passengers in the second journey will be the remaining people after the first journey.
To find the number of ways, we need to consider all possible combinations for the number of passengers in the first journey and calculate the corresponding number of passengers in the second journey.
To calculate combinations, we use the formula:
C(n, r) = n! / (r! * (n - r)!),
where n is the total number of elements, and r is the number of selected elements.
Let's apply this formula to our scenario:
1. For the first journey:
- If 0 passengers are taken in the first journey, then 13 passengers will be left for the second journey.
- If 1 passenger is taken in the first journey, then 12 passengers will be left for the second journey.
- And so on, until 8 passengers.
2. For the second journey:
- If 0 passengers are taken in the second journey, then the number of passengers taken in the first journey is 13.
- If 1 passenger is taken in the second journey, then the number of passengers taken in the first journey is 12.
- And so on, until 8 passengers.
We will now calculate the number of combinations for each scenario and sum them up to get the total number of ways the lift can carry the group of 13 people in two journeys.
Total number of ways = C(13, 0) * C(13, 13) + C(13, 1) * C(12, 12) + C(13, 2) * C(11, 11) + ... + C(13, 8) * C(5, 5).
By applying the combination formula to each term and adding them, we can calculate the total number of ways the lift can carry the group of 13 people in two journeys.