Permutation and Combination (In how many ways possible?)

Question

8 male and 5 female mathematics teachers applied for a teaching position. Only 6 teachers will be accepted. In how many ways can they be employed if 3 males are to be chosen?

Choices:

a. 420             b. 560             c. 620             d. 760

Solution:

(Please show solution aswell)

Answer 1

If 3 and only 3 male teachers are to be chosen, then you can choose the male teachers first. Then the combinations are

₈C₃ = 56

Then you are left with choosing 3 female teachers. Then the combinations are

₅C₃ = 10

So the total number of combinations is 56*10 = 560