CPhill

Looking at the 4 x 4  face, we have  4 x (5 - 2) = 4 x  3  = 12   "inner cubes"  that will have no paint on them

The total number of committees that can be formed = C(25,5)  = 53130

And from this we just want to subtract all the commitees that can  be formed solely of boys  = C(10,5) = 252 and all the committees that can be formed solely of girls  = C(15,5)  = 3003

So.....the probability of a committee with at least one boy and one girl  =

[ 53130 - 252 - 3003] / 53130  = .9387  = 93.87%

Let the area of the living room  =  A

So

35  =  (1/5)A - 25          add 25 to both sides

60  =  (1/5)A        multiply both sides by 5

5 * 60  = A  =  300 sq ft

Since only the x coordinate changes, B is a reflection of A across the y axis

(x + 4) / 4  =  (x + 3 ) / 3   cross-multiply

3(x + 4)  = 4(x + 3)  simplify

3x + 12  =  4x + 12     subtract 12 from both sides

3x =  4x         subtract 3x from both sides

0 = 4x - 3x

0  = 1x          divide both sides by 1

0  =  x

3245 / 5.5  = 590  ......no rounding necessary....!!!!!

Each successive term is 5 less than the previous term

The nth term, a_n, is given by :

a_n = 2 - 5(n - 1)

You are correct Mathguardian....Good Job.......!!!!!

(x + 1)^x+1  =

C(x + 1, 0) * x^{x+ 1}  + C(x+1, 1) * x^x  + C(x + 1, 2) * x^x-1 +.......+ C(x +1, x -1) * x² + C(x + 1, x) * x  +

C(x + 1, x + 1) * x⁰ * 1^x

Note that the first term just evaluates to x^{x + 1} and the last term just  evaluates to 1

HAHAHA!!.....yeah...if you're amongst the "Flat Earthers"....then your procedure is "valid"....