A multiple choice exam has 10 questions. Each question has 4 possible answers, of which only 1 is correct. If a student guesses on each question, what is the probability that the student will get exactly 6 questions correct?

Step 1 ：Step 1: Identify the values for the formula of binomial distribution. In this case, n (number of trials) is 10, k (number of successes) is 6, and p (probability of success on a single trial) is 0.25 (since there's 1 correct answer out of 4).

Step 2 ：Step 2: Plug these values into the formula for the binomial probability: $P(X=k)=C(n,k)\ast p^k\ast (1-p{)}^{n-k}$

Step 3 ：Step 3: Calculate the binomial coefficient C(n, k) which is $C(10,6)=\frac{10!}{6!(10-6)!}=210$

Step 4 ：Step 4: Calculate $p^k=(0.25{)}^6=0.000244140625$

Step 5 ：Step 5: Calculate $(1-p{)}^{n-k}=(0.75{)}^4=0.31640625$

Step 6 ：Step 6: Multiply all these values together to find the probability: $P(X=6)=210\ast 0.000244140625\ast 0.31640625=0.01614$