Afair die is rolled 8 times. a. what is the probability that the die comes up 6 exactly twice?

P(first 2 rolls = 6 and rest not 6)  = 1/6 * 1/6 * (5/6)^6 =   0.00930272

there are 8C2 ways  of obtaining  exactly 2 6's in 8 throws = 28 ways

so required probability is 0.00930272 * 28 =  0.26  to nearest hundredth

31 is prime. and it’s prime factorization is just 31.