Atraffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds.
if 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is

If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is:

                                  0.25412184

Here we need to use the binomial theorem.

i.e. the probability of k successes out of total n experiments is calculated by the formula:

where p is the probability of successes.

Here we have p=Probability that signal is red.

i.e. p=15/50=3/10=0.3

Hence, 1-p=0.7

Also we have: n=8

and k=3

Hence,

                  Hence, the probability is:

                       0.25412184

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

i dont know

step-by-step explanation: