The result of rolling a number cube 7 times is a 7-digit number composed of digits 1,2,3,4,5 and 6 so that digits can repeat. The total number of possibilities is 6^7.
The number of possibilities where 4 appears exactly two times is 5^5*(7!-6!/2). 5^5 is the number of 5-digits numbers composed of digits 1,2,3,5 and 6 so that digits can repeat. 7! is the number of permutations of digits 1,2,3,4,4,5 and 6. 6! is the number of permutations of digits 1,2,3,{4,4},5 and 6. We don't want to subtract all numbers where digits 4 appear side by side. That's why we must divide 6! by 2.
You can probably figure out the rectangle of 16 by 8 so no explaining there. 16×8=128. You know that diameter of the cirkel is equal to y so 8. The diameter of a cirkel is two times its radius. so 8=2r. r=4. The area of a cirkel is calculated by the formula \pi×r^2. Fill in r=4 in \pi×r^2 gives us \pi×4^2=16\pi. You only have half of the cirkel so 16\pi/2=8\pi. 128+8\pi=153.12 which is A.
