Question

Compute the permutations and combinations. a farmer buys 2 cows, 3 pigs, and 10 sheep from a seller who has 7 cows, 4 pigs, and 10 sheep. how many choices of animals does he have?

Answer 1

the farmer has 26 choices

Answer 2

Total number of ways = 84

Explanation:

Number of choices farmer has for cows = 2 out of 7

Number of choices farmer has for pigs = 3 out of 4

Number of choices farmer has for cows = 10 out of 10

`\text{Number of ways of choosing cows = }_2^7\txterm{C}=21`

`\text{Number of ways of choosing cows = }_3^4\txterm{C}=4`

`\text{Number of ways of choosing cows = }_(10)^(10)\txterm{C}=1`

All these three groups of different animals can make different groups when taken together

Thus, Total number of ways = 21 × 4 × 1

⇒ Total number of ways = 84