A farmer buys 3 cows, 2 goats, and 4 hens from a man who has 6 cows, 5 goats, and 8 hens.
How many ways the farmer choose his desired animals?
To determine the number of ways the farmer can choose his desired animals, we need to find the number of possible combinations for each type of animal.
For the cows:
The farmer can choose 3 out of the 6 cows. This can be calculated using the combination formula C(n, r), where n is the total number of cows and r is the number of cows the farmer wants to choose:
C(6, 3) = 6! / (3! * (6-3)!) = 20
For the goats:
The farmer can choose 2 out of the 5 goats:
C(5, 2) = 5! / (2! * (5-2)!) = 10
For the hens:
The farmer can choose 4 out of the 8 hens:
C(8, 4) = 8! / (4! * (8-4)!) = 70
To calculate the total number of ways the farmer can choose his desired animals, we need to multiply the number of combinations for each type of animal:
20 * 10 * 70 = 14,000
Therefore, there are 14,000 ways the farmer can choose his desired animals.
To determine the number of ways the farmer can choose his desired animals, we need to calculate the number of combinations of cows, goats, and hens that the farmer can select.
The farmer can choose 3 cows from a pool of 6 cows in 6C3 ways.
The farmer can choose 2 goats from a pool of 5 goats in 5C2 ways.
The farmer can choose 4 hens from a pool of 8 hens in 8C4 ways.
To find the total number of ways, we multiply the number of ways for each selection:
6C3 * 5C2 * 8C4
Now, let's solve each term step-by-step:
6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2) = 20
5C2 = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10
8C4 = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70
Now, multiply these three terms together:
20 * 10 * 70 = 14,000
Therefore, the farmer can choose his desired animals in 14,000 different ways.
To find out the number of ways the farmer can choose his desired animals, we need to determine the possible combinations of cows, goats, and hens that can be chosen.
The farmer wants to buy 3 cows, 2 goats, and 4 hens. From the man, there are 6 cows, 5 goats, and 8 hens available.
We can solve this problem using combinatorics. The number of ways to choose x items from a set of n items is given by the combination formula, nCx = n! / (x!(n-x)!), where n! denotes the factorial of n.
Let's calculate the number of ways to choose the desired animals:
1. Number of ways to choose 3 cows from 6: 6C3 = 6! / (3!(6-3)!) = 6! / (3!3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20
2. Number of ways to choose 2 goats from 5: 5C2 = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4) / (2 * 1) = 10
3. Number of ways to choose 4 hens from 8: 8C4 = 8! / (4!(8-4)!) = 8! / (4!4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70
To find the total number of ways to choose the desired animals, we need to find the product of all the combinations:
Total ways = 20 * 10 * 70 = 14,000
Therefore, there are 14,000 ways the farmer can choose his desired animals.