Question

A farmer wants to take 4 of his animals to a city. He has to select the animals  from 5 cows and 5 goats.  (a) How many possible selections can he make?  (b) In how many of these selections will there be more cows than goats?​

Answer 1

(a) 210

(b) 55

Explanation:

(a) I'm assuming the animals are considered to be unique rather than identical. The order of the animals isn't important, so the number of ways he can choose 4 animals from 10 is:

₁₀C₄ = 210

(b) If there are more cows than goats, then there are either 3 cows and 1 goat:

₅C₃ ₅C₁ = 50

Or there are 4 cows:

₅C₄ = 5

The total number of combinations is 55.