31. There are C(5, 2) = 10 ways to choose 2 colors from a group of 10 colors if you don't care about the order. (Here, we treat blue background with violet letters as being indistinguishable from violet background with blue letters.)
Only one of those 10 pairs is "B and V", so the probability is 1/10.
a) P(B and V) = 10%
32. The 12 inch dimension on the figure is 0 inches for the cross section. The remaining dimensions of the cross section are
c) 5 in. × 4 in.
_____
C(n, k) = n!/(k!·(n-k)!)
C(5, 2) = 5!/(2!·3!) = 5·4/(2·1) = 10
Let x = amount of time the Arlen family must catch up to
overtake the Harris family
In principle, the Harris and the Arlen family should cover
the same distance. Since distance is speed x time,
45 (6+y) = 58y
270 + 45y = 58y
58y - 45y = 270
y = 270 ÷ 13
y= 20.77min
-6×-6=36
f-34=36
34+36=70
f=70
