The rooms of Ben’s apartment has 14 walls. He has enough paint to cover 10 of these walls with one color and the rest with another color. In how many ways could Ben paint his apartment ?

Answer 1

If he only has enough to paint 14 walls, then there are 14C10 ways to pick the 10 walls for color #1.

If he enough of the 2nd color to paint any or all of the walls, then
color1 + color2
10+4: 14C10
9+5: 14C9
...
1+13: 14C1
0+14: 1
Now add them all up

Answer 2

14C10 for the first 10 - first color
14C4 for rest of the walls (4) second color

14C10+14C4

That was my understanding ...

10+4: 14C10
9+5: 14C9
...
1+13: 14C1
0+14: 1

could not follow .... Thx

Answer 3

since you only have two colors, the 14C10 ways to choose the 1st color walls leaves you no choice for the 2nd color. You always have to pick all 4 of the unchosen walls, right?

Answer 4

Thank you Pal,

Kind of confused . If you can be more specific I appreciate.