a city council has 12 members. Five are democratss and seven are republicans. How many ways can a four member comitte be selected?

Answer: 495ways

Step-by-step explanation:

Selecting some b people from a group of people are based on combination principle.

If we are selecting "r'' people from a total number of 'n' people, we will have;

nCr = n! / (n-r) ! r!

Since 4 people are to be selected from a committee of 5democrats and 6republicans,

Note that the question is not specific as to how many from Republicans and Democrats to select that will make the 4people,

Therefore, the selection can be done in this manner

- 0people from democrats and 4peoples from Republicans

5C0 * 7C4 = 5!/5!0! * 7!/3!4!

= 1*35 = 35ways

- 1people from democrats and 3peoples from Republicans

5C1 * 7C3 = 5*35 = 175ways

- 2peoples from democrats and 2peoples from Republicans

5C2 * 7C2 = 10 * 21 = 210ways

- 3peoples from democrats and 1people from Republicans

5C3 * 7C1 = 10 * 7 = 70ways

- 4peoples from democrats and 0people from Republicans

5C4 * 7C0 = 5 * 1 = 5ways

Adding all possible combinations

35+175+210+70+5

= 495ways